8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7a65555e-1bb2-4947-8e70-50f267017bfd-24_442_1167_341_548}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
One end of a light inextensible string is attached to a particle \(A\) of mass \(2 m\). The other end of the string is attached to a particle \(B\) of mass \(3 m\). Particle \(A\) is held at rest on a rough plane which is inclined to horizontal ground at an angle \(\alpha\), where \(\tan \alpha = \frac { 5 } { 12 }\) The string passes over a small smooth pulley \(P\) which is fixed at the top of the plane. Particle \(B\) hangs vertically below \(P\) with the string taut, at a height \(h\) above the ground, as shown in Figure 4.
The part of the string between \(A\) and \(P\) lies along a line of greatest slope of the plane. The two particles, the string and the pulley all lie in the same vertical plane.
The coefficient of friction between \(A\) and the plane is \(\frac { 11 } { 36 }\)
The particle \(A\) is released from rest and begins to move up the plane.
- Show that the frictional force acting on \(A\) as it moves up the plane is \(\frac { 22 m g } { 39 }\)
- Write down an equation of motion for \(B\).
- Show that the acceleration of \(A\) immediately after its release is \(\frac { 1 } { 3 } g\)
In the subsequent motion, \(A\) comes to rest before it reaches the pulley.
- Find, in terms of \(h\), the total distance travelled by \(A\) from when it was released from rest to when it first comes to rest again.
| VJYV SIHI NI JIIIM ION OC | vauv sthin NI BLIYM ION OC | V34V SIHI NI IIIIMM ION OC |
| VJYV SIHI NI JIIIM ION OC | vauv sthin NI BLIYM ION OO | V34V SIHI NI IIIIMM ION OC |