1 A particle is projected with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(60 ^ { \circ }\) above the horizontal. Calculate the time after projection when the particle is descending at an angle of \(40 ^ { \circ }\) below the horizontal.
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\caption{Fig. 1}
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One end of a light inextensible string is attached to a fixed point \(A\). The other end of the string is attached to a particle \(P\) of mass \(m \mathrm {~kg}\) which hangs vertically below \(A\). The particle is also attached to one end of a light elastic string of natural length 0.25 m . The other end of this string is attached to a point \(B\) which is 0.6 m from \(P\) and on the same horizontal level as \(P\). Equilibrium is maintained by a horizontal force of magnitude 7 N applied to \(P\) (see Fig. 1).
- Calculate the modulus of elasticity of the elastic string.
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\caption{Fig. 2}
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\(P\) is released from rest by removing the 7 N force. In its subsequent motion \(P\) first comes to instantaneous rest at a point where \(B P = 0.3 \mathrm {~m}\) and the elastic string makes an angle of \(30 ^ { \circ }\) with the horizontal (see Fig. 2). - Find the value of \(m\).