Questions — Edexcel M1 (599 questions)

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Edexcel M1 2016 June Q1
  1. A car is moving along a straight horizontal road with constant acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 } ( a > 0 )\). At time \(t = 0\) the car passes the point \(P\) moving with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). In the next 4 s , the car travels 76 m and then in the following 6 s it travels a further 219 m .
Find
  1. the value of \(u\),
  2. the value of \(a\).
Edexcel M1 2016 June Q2
  1. Two particles \(P\) and \(Q\) are moving in opposite directions along the same horizontal straight line. Particle \(P\) has mass \(m\) and particle \(Q\) has mass \(k m\). The particles collide directly. Immediately before the collision, the speed of \(P\) is \(u\) and the speed of \(Q\) is \(2 u\). As a result of the collision, the direction of motion of each particle is reversed and the speed of each particle is halved.
    1. Find the value of \(k\).
      (4)
    2. Find, in terms of \(m\) and \(u\) only, the magnitude of the impulse exerted on \(Q\) by \(P\) in the collision.
      (2)
    3. A block \(A\) of mass 9 kg is released from rest from a point \(P\) which is a height \(h\) metres above horizontal soft ground. The block falls and strikes another block \(B\) of mass 1.5 kg which is on the ground vertically below \(P\). The speed of \(A\) immediately before it strikes \(B\) is \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The blocks are modelled as particles.
    4. Find the value of \(h\).
      (2)
    Immediately after the impact the blocks move downwards together with the same speed and both come to rest after sinking a vertical distance of 12 cm into the ground. Assuming that the resistance offered by the ground has constant magnitude \(R\) newtons,
  2. find the value of \(R\).
    (8)
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Edexcel M1 2016 June Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{55024b00-68f0-4f8b-9b08-58479bb291fd-06_244_1168_264_388} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A diving board \(A B\) consists of a wooden plank of length 4 m and mass 30 kg . The plank is held at rest in a horizontal position by two supports at the points \(A\) and \(C\), where \(A C = 0.6 \mathrm {~m}\), as shown in Figure 1. The force on the plank at \(A\) acts vertically downwards and the force on the plank at \(C\) acts vertically upwards. A diver of mass 50 kg is standing on the board at the end \(B\). The diver is modelled as a particle and the plank is modelled as a uniform rod. The plank is in equilibrium.
  1. Find
    1. the magnitude of the force acting on the plank at \(A\),
    2. the magnitude of the force acting on the plank at \(C\). The support at \(A\) will break if subjected to a force whose magnitude is greater than 5000 N .
  2. Find, in kg, the greatest integer mass of a diver who can stand on the board at \(B\) without breaking the support at \(A\).
  3. Explain how you have used the fact that the diver is modelled as a particle.
Edexcel M1 2016 June Q5
5. Two forces, \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\), act on a particle \(A\).
\(\mathbf { F } _ { 1 } = ( 2 \mathbf { i } - 3 \mathbf { j } ) \mathrm { N }\) and \(\mathbf { F } _ { 2 } = ( p \mathbf { i } + q \mathbf { j } ) \mathrm { N }\), where \(p\) and \(q\) are constants.
Given that the resultant of \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\) is parallel to ( \(\mathbf { i } + 2 \mathbf { j }\) ),
  1. show that \(2 p - q + 7 = 0\) Given that \(q = 11\) and that the mass of \(A\) is 2 kg , and that \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\) are the only forces acting on \(A\),
  2. find the magnitude of the acceleration of \(A\).
Edexcel M1 2016 June Q6
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{55024b00-68f0-4f8b-9b08-58479bb291fd-09_264_997_269_461} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Two cars, \(A\) and \(B\), move on parallel straight horizontal tracks. Initially \(A\) and \(B\) are both at rest with \(A\) at the point \(P\) and \(B\) at the point \(Q\), as shown in Figure 2. At time \(t = 0\) seconds, \(A\) starts to move with constant acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for 3.5 s , reaching a speed of \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Car \(A\) then moves with constant speed \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  1. Find the value of \(a\). Car \(B\) also starts to move at time \(t = 0\) seconds, in the same direction as car \(A\). Car \(B\) moves with a constant acceleration of \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). At time \(t = T\) seconds, \(B\) overtakes \(A\). At this instant \(A\) is moving with constant speed.
  2. On a diagram, sketch, on the same axes, a speed-time graph for the motion of \(A\) for the interval \(0 \leqslant t \leqslant T\) and a speed-time graph for the motion of \(B\) for the interval \(0 \leqslant t \leqslant T\).
  3. Find the value of \(T\).
  4. Find the distance of car \(B\) from the point \(Q\) when \(B\) overtakes \(A\).
  5. On a new diagram, sketch, on the same axes, an acceleration-time graph for the motion of \(A\) for the interval \(0 \leqslant t \leqslant T\) and an acceleration-time graph for the motion of \(B\) for the interval \(0 \leqslant t \leqslant T\).
Edexcel M1 2016 June Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{55024b00-68f0-4f8b-9b08-58479bb291fd-11_570_1045_262_459} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A particle \(P\) of mass 4 kg is attached to one end of a light inextensible string. A particle \(Q\) of mass \(m \mathrm {~kg}\) is attached to the other end of the string. The string passes over a small smooth pulley which is fixed at a point on the intersection of two fixed inclined planes. The string lies in a vertical plane that contains a line of greatest slope of each of the two inclined planes. The first plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\) and the second plane is inclined to the horizontal at an angle \(\beta\), where \(\tan \beta = \frac { 4 } { 3 }\). Particle \(P\) is on the first plane and particle \(Q\) is on the second plane with the string taut, as shown in Figure 3. The first plane is rough and the coefficient of friction between \(P\) and the plane is \(\frac { 1 } { 4 }\). The second plane is smooth. The system is in limiting equilibrium. Given that \(P\) is on the point of slipping down the first plane,
  1. find the value of \(m\),
  2. find the magnitude of the force exerted on the pulley by the string,
  3. find the direction of the force exerted on the pulley by the string.
Edexcel M1 2017 June Q1
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c3869c7-008f-4131-b68d-8ecdd4da3377-02_346_499_251_721} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A particle \(P\) of weight 5 N is attached to one end of a light string. The other end of the string is attached to a fixed point \(O\). A force of magnitude \(F\) newtons is applied to \(P\). The line of action of the force is inclined to the horizontal at \(30 ^ { \circ }\) and lies in the same vertical plane as the string. The particle \(P\) is in equilibrium with the string making an angle of \(40 ^ { \circ }\) with the downward vertical, as shown in Figure 1. Find
  1. the tension in the string,
  2. the value of \(F\).
Edexcel M1 2017 June Q2
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c3869c7-008f-4131-b68d-8ecdd4da3377-04_429_1298_255_324} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A wooden beam \(A B\) has weight 140 N and length \(2 a\) metres. The beam rests horizontally in equilibrium on two supports at \(C\) and \(D\), where \(A C = 2 \mathrm {~m}\) and \(A D = 6 \mathrm {~m}\). A block of weight 30 N is placed on the beam at \(B\) and the beam remains horizontal and in equilibrium, as shown in Figure 2. The reaction on the beam at \(D\) has magnitude 120 N . The block is modelled as a particle and the beam is modelled as a uniform rod.
  1. Find the value of \(a\). The support at \(D\) is now moved to a point \(E\) on the beam and the beam remains horizontal and in equilibrium with the block at \(B\). The magnitude of the reaction on the beam at \(C\) is now equal to the magnitude of the reaction on the beam at \(E\).
  2. Find the distance \(A E\).
Edexcel M1 2017 June Q3
3. Two particles, \(P\) and \(Q\), have masses 0.5 kg and \(m \mathrm {~kg}\) respectively. They are moving in opposite directions towards each other along the same straight line on a smooth horizontal plane and collide directly. Immediately before the collision the speed of \(P\) is \(4 \mathrm {~ms} ^ { - 1 }\) and the speed of \(Q\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The magnitude of the impulse exerted on \(P\) by \(Q\) in the collision is 4.2 N s . As a result of the collision the direction of motion of \(P\) is reversed.
  1. Find the speed of \(P\) immediately after the collision. The speed of \(Q\) immediately after the collision is \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  2. Find the two possible values of \(m\).
Edexcel M1 2017 June Q4
  1. A small ball of mass 0.2 kg is moving vertically downwards when it hits a horizontal floor. Immediately before hitting the floor the ball has speed \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Immediately after hitting the floor the ball rebounds vertically with speed \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    1. Find the magnitude of the impulse exerted by the floor on the ball.
    By modelling the motion of the ball as that of a particle moving freely under gravity,
  2. find the maximum height above the floor reached by the ball after it has rebounded from the floor,
  3. find the time between the instant when the ball first hits the floor and the instant when the ball is first 1 m above the floor and moving upwards.
Edexcel M1 2017 June Q5
  1. Two trains, \(P\) and \(Q\), move on horizontal parallel straight tracks. Initially both are at rest in a station and level with each other. At time \(t = 0 , P\) starts off and moves with constant acceleration for 10 s up to a speed of \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and then moves at a constant speed of \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At time \(t = 20\), where \(t\) is measured in seconds, train \(Q\) starts to move in the same direction as \(P\). Train \(Q\) accelerates with the same initial constant acceleration as \(P\), up to a speed of \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and then moves at a constant speed of \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Train \(Q\) overtakes \(P\) at time \(t = T\), after both trains have reached their constant speeds.
    1. Sketch, on the same axes, the speed-time graphs of both trains for \(0 \leqslant t \leqslant T\).
    2. Find the value of \(t\) at the instant when both trains are moving at the same speed.
    3. Find the value of \(T\).
Edexcel M1 2017 June Q6
  1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors due east and due north respectively.]
A particle \(P\) moves with constant acceleration \(( - 2 \mathbf { i } + 3 \mathbf { j } ) \mathrm { ms } ^ { - 2 }\). At time \(t\) seconds, the velocity of \(P\) is \(\mathbf { v m ~ s } ^ { - 1 }\). When \(t = 0 , \mathbf { v } = 10 \mathbf { i } + 4 \mathbf { j }\).
  1. Find the direction of motion of \(P\) when \(t = 6\), giving your answer as a bearing to the nearest degree.
  2. Find the value of \(t\) when \(P\) is moving north east.
Edexcel M1 2017 June Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c3869c7-008f-4131-b68d-8ecdd4da3377-22_254_291_251_831} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Two forces, \(\mathbf { P }\) and \(\mathbf { Q }\), act on a particle. The force \(\mathbf { P }\) has magnitude 8 N and the force \(\mathbf { Q }\) has magnitude 5 N . The angle between the directions of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(50 ^ { \circ }\), as shown in Figure 3. The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) is the force \(\mathbf { R }\).
  1. Find, to 3 significant figures, the magnitude of \(\mathbf { R }\).
  2. Find, to the nearest degree, the size of the angle between the direction of \(\mathbf { P }\) and the direction of \(\mathbf { R }\).
Edexcel M1 2017 June Q8
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c3869c7-008f-4131-b68d-8ecdd4da3377-24_369_1200_248_370} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Two particles, \(P\) and \(Q\), with masses \(2 m\) and \(m\) respectively, are attached to the ends of a light inextensible string. The string passes over a small smooth pulley which is fixed at the edge of a rough horizontal table. Particle \(Q\) is held at rest on the table and particle \(P\) is on the surface of a smooth inclined plane. The top of the plane coincides with the edge of the table. The plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\), as shown in Figure 4. The string lies in a vertical plane containing the pulley and a line of greatest slope of the plane. The coefficient of friction between \(Q\) and the table is \(\frac { 1 } { 2 }\). Particle \(Q\) is released from rest with the string taut and \(P\) begins to slide down the plane.
  1. By writing down an equation of motion for each particle,
    1. find the initial acceleration of the system,
    2. find the tension in the string. Suppose now that the coefficient of friction between \(Q\) and the table is \(\mu\) and when \(Q\) is released it remains at rest.
  2. Find the smallest possible value of \(\mu\).
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    Q8

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Edexcel M1 2018 June Q1
  1. Particle \(P\) has mass \(3 m\) and particle \(Q\) has mass \(m\). The particles are moving towards each other in opposite directions along the same straight line on a smooth horizontal plane. The particles collide directly. Immediately before the collision the speed of \(P\) is \(u\) and the speed of \(Q\) is \(3 u\). In the collision, the magnitude of the impulse exerted by \(Q\) on \(P\) is \(5 m u\).
    1. Find the speed of \(P\) immediately after the collision.
    2. Find the speed of \(Q\) immediately after the collision.
Edexcel M1 2018 June Q2
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c0993853-dd8f-4d14-aeed-b71ad60df09c-04_360_1037_260_456} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A uniform wooden beam \(A B\), of mass 20 kg and length 4 m , rests in equilibrium in a horizontal position on two supports. One support is at \(C\), where \(A C = 1.6 \mathrm {~m}\), and the other support is at \(D\), where \(D B = 0.4 \mathrm {~m}\). A boy of mass 60 kg stands on the beam at the point \(P\), where \(A P = 3 \mathrm {~m}\), as shown in Figure 1. The beam remains in equilibrium in a horizontal position. By modelling the boy as a particle and the beam as a uniform rod,
    1. find, in terms of \(g\), the magnitude of the force exerted on the beam by the support at \(C\),
    2. find, in terms of \(g\), the magnitude of the force exerted on the beam by the support at \(D\). The boy now starts to walk slowly along the beam towards the end \(A\).
  2. Find the greatest distance he can walk from \(P\) without the beam tilting.
Edexcel M1 2018 June Q3
3. A cyclist starts from rest at the point \(O\) on a straight horizontal road. The cyclist moves along the road with constant acceleration \(2 \mathrm {~ms} ^ { - 2 }\) for 4 seconds and then continues to move along the road at constant speed. At the instant when the cyclist stops accelerating, a motorcyclist starts from rest at the point \(O\) and moves along the road with constant acceleration \(4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) in the same direction as the cyclist. The motorcyclist has been moving for \(T\) seconds when she overtakes the cyclist.
  1. Sketch, on the same axes, a speed-time graph for the motion of the cyclist and a speed-time graph for the motion of the motorcyclist, to the time when the motorcyclist overtakes the cyclist.
  2. Find, giving your answer to 1 decimal place, the value of \(T\).
Edexcel M1 2018 June Q4
4. A rough plane is inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\). A particle of mass 2 kg is projected with speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(O\) on the plane, up a line of greatest slope of the plane. The coefficient of friction between the particle and the plane is 0.25
  1. Find the magnitude of the frictional force acting on the particle as it moves up the plane. The particle comes to instantaneous rest at the point \(A\).
  2. Find the distance \(O A\). The particle now moves down the plane from \(A\).
  3. Find the speed of \(P\) as it passes through \(O\).
Edexcel M1 2018 June Q5
5. [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular horizontal unit vectors and position vectors are given relative to a fixed origin \(O\).] A particle \(P\) is moving in a straight line with constant velocity. At 9 am, the position vector of \(P\) is \(( 7 \mathbf { i } + 5 \mathbf { j } ) \mathrm { km }\) and at 9.20 am , the position vector of \(P\) is \(6 \mathbf { i } \mathrm {~km}\). At time \(t\) hours after 9 am , the position vector of \(P\) is \(\mathbf { r } _ { P } \mathrm {~km}\).
  1. Find, in \(\mathrm { kmh } ^ { - 1 }\), the speed of \(P\).
  2. Show that \(\mathbf { r } _ { P } = ( 7 - 3 t ) \mathbf { i } + ( 5 - 15 t ) \mathbf { j }\).
  3. Find the value of \(t\) when \(\mathbf { r } _ { P }\) is parallel to \(16 \mathbf { i } + 5 \mathbf { j }\). The position vector of another particle \(Q\), at time \(t\) hours after 9 am , is \(\mathbf { r } _ { Q } \mathrm {~km}\), where \(\mathbf { r } _ { Q } = ( 5 + 2 t ) \mathbf { i } + ( - 3 + 5 t ) \mathbf { j }\)
  4. Show that \(P\) and \(Q\) will collide and find the position vector of the point of collision.
Edexcel M1 2018 June Q6
6. A car pulls a trailer along a straight horizontal road using a light inextensible towbar. The mass of the car is \(M \mathrm {~kg}\), the mass of the trailer is 600 kg and the towbar is horizontal and parallel to the direction of motion. There is a resistance to motion of magnitude 200 N acting on the car and a resistance to motion of magnitude 100 N acting on the trailer. The driver of the car spots a hazard ahead. Instantly he reduces the force produced by the engine of the car to zero and applies the brakes of the car. The brakes produce a braking force on the car of magnitude 6500 N and the car and the trailer have a constant deceleration of magnitude \(4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) Given that the resistances to motion on the car and trailer are unchanged and that the car comes to rest after travelling 40.5 m from the point where the brakes were applied, find
  1. the thrust in the towbar while the car is braking,
  2. the value of \(M\),
  3. the time it takes for the car to stop after the brakes are applied.
Edexcel M1 2018 June Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c0993853-dd8f-4d14-aeed-b71ad60df09c-24_206_1040_356_443} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A washing line \(A B C D\) is fixed at the points \(A\) and \(D\). There are two heavy items of clothing hanging on the washing line, one fixed at \(B\) and the other fixed at \(C\). The washing line is modelled as a light inextensible string, the item at \(B\) is modelled as a particle of mass 3 kg and the item at \(C\) is modelled as a particle of mass \(M \mathrm {~kg}\). The section \(A B\) makes an angle \(\alpha\) with the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\), the section \(B C\) is horizontal and the section \(C D\) makes an angle \(\beta\) with the horizontal, where \(\tan \beta = \frac { 12 } { 5 }\), as shown in Figure 2. The system is in equilibrium.
  1. Find the tension in \(A B\).
  2. Find the tension in BC.
  3. Find the value of \(M\).
    END
Edexcel M1 2020 June Q1
  1. Two particles, \(P\) and \(Q\), with masses \(m\) and \(2 m\) respectively, are moving in the same direction along the same straight line when they collide directly. Immediately before they collide, \(P\) is moving with speed \(4 u\) and \(Q\) is moving with speed \(u\). Immediately after they collide, both particles are moving in the same direction and the speed of \(Q\) is four times the speed of \(P\).
    1. Find the speed of \(Q\) immediately after the collision.
    2. Find the magnitude of the impulse exerted by \(Q\) on \(P\) in the collision.
    3. State clearly the direction of this impulse.
Edexcel M1 2020 June Q2
2. A small ball is thrown vertically upwards with speed \(14.7 \mathrm {~ms} ^ { - 1 }\) from a point that is 19.6 m above horizontal ground. The ball is modelled as a particle moving freely under gravity. Find
  1. the total time from when the ball is thrown to when it first hits the ground,
  2. the speed of the ball immediately before it first hits the ground,
  3. the total distance travelled by the ball from when it is thrown to when it first hits the ground.
  4. Sketch a velocity-time graph for the motion of the ball from when it is thrown to when it first hits the ground. State the coordinates of the start point and the coordinates of the end point of your graph.
    DO NOT WRITEIN THIS AREA
Edexcel M1 2020 June Q3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05cf68a3-1ba4-487f-9edd-48a246f4194f-08_259_597_214_678} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A particle of mass 10 kg is placed on a fixed rough inclined plane. The plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\). The particle is held in equilibrium by a force of magnitude \(P\) newtons, which acts up the plane, as shown in Figure 1. The line of action of the force lies in a vertical plane that contains a line of greatest slope of the plane. The coefficient of friction between the particle and the plane is \(\frac { 1 } { 2 }\).
  1. Find the normal reaction between the particle and the plane.
  2. Find the greatest possible value of \(P\).
  3. Find the least possible value of \(P\). DO NOT WRITEIN THIS AREA
    VIXV SIHIANI III IM IONOOVIAV SIHI NI JYHAM ION OOVI4V SIHI NI JLIYM ION OO
Edexcel M1 2020 June Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05cf68a3-1ba4-487f-9edd-48a246f4194f-12_536_1253_127_349} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A non-uniform beam \(A B\) has length 8 m and mass \(M \mathrm {~kg}\). The centre of mass of the beam is \(d\) metres from \(A\). The beam is supported in equilibrium in a horizontal position by two vertical light ropes. One rope is attached to the beam at \(C\), where \(A C = 2.5 \mathrm {~m}\) and the other rope is attached to the beam at \(D\), where \(D B = 2 \mathrm {~m}\), as shown in Figure 2. A gymnast, of mass 64 kg , stands on the beam at the point \(X\), where \(A X = 1.875 \mathrm {~m}\), and the beam remains in equilibrium in a horizontal position but is now on the point of tilting about \(C\). The gymnast then dismounts from the beam. A second gymnast, of mass 48 kg , now stands on the beam at the point \(Y\), where \(Y B = 0.5 \mathrm {~m}\), and the beam remains in equilibrium in a horizontal position but is now on the point of tilting about \(D\). The beam is modelled as a non-uniform rod and the gymnasts are modelled as particles. Find the value of \(M\).
VIXV SIHIANI III IM IONOOVIAV SIHI NI JYHAM ION OOVI4V SIHI NI JLIYM ION OO