A ball is thrown vertically downward from a height of \(20\) m with an initial velocity \(v_0\). It collides with the ground, loses \(50\%\) of its energy in a collision, and rebounds to the same height. The initial velocity \(v_0\) is:
[Take, \(g=10~\mathrm{ms^{-2}}\)]
1. \(14\) ms-1
2. \(20\) ms-1
3. \(28\) ms-1
4. \(10\) ms-1
Two similar springs \(P\) and \(Q\) have spring constants \(k_P\) and \(k_Q\), such that \(k_P>k_Q\). They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs \(W_P\) and \(W_Q\) are related as, in case (a) and case (b), respectively:
1. \(W_P=W_Q;~W_P>W_Q\)
2. \(W_P=W_Q;~W_P=W_Q\)
3. \(W_P>W_Q;~W_P<W_Q\)
4. \(W_P<W_Q;~W_P<W_Q\)
A block of mass \(10\) kg, moving in the x-direction with a constant speed of \(10\) ms-1 is subjected to a retarding force \(F=0.1x\) J/m during its travel from \(x = 20\) m to \(30\) m. Its final kinetic energy will be:
1. \(475\) J
2. \(450\) J
3. \(275\) J
4. \(250\) J
A particle of mass \(m\) is driven by a machine that delivers a constant power of \(k\) watts. If the particle starts from rest, the force on the particle at time \(t\) is:
1. \(
\sqrt{\frac{m k}{2}} t^{-1 / 2}
\)
2. \( \sqrt{m k} t^{-1 / 2}
\)
3. \( \sqrt{2 m k} t^{-1 / 2}
\)
4. \( \frac{1}{2} \sqrt{m k} t^{-1 / 2}\)
Two particles of masses m1 and m2 move with initial velocities u1 and u2 respectively. On collision, one of the particles gets excited to a higher level, after absorbing energy E. If the final velocities of particles are v1 and v2, then we must have:
1.
2.
3.
4.
On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of the same mass M which is initially at rest. After the collision, the first block moves at an angle to its initial direction and has a speed . The second block’s speed after the collision will be:
1.
2.
3.
4.
A uniform force of \((3 \hat{i} + \hat{j})\) newton acts on a particle of mass \(2\) kg. Hence the particle is displaced from position \((2 \hat{i} + \hat{k})\) meter to position \((4 \hat{i} + 3 \hat{j} - \hat{k})\) meter. The work done by the force on the particle is:
1. \(6\) J
2. \(13\) J
3. \(15\) J
4. \(9\) J
The potential energy of a particle in a force field is \(U=\) where \(A\) and \(B\) are positive constants and \(r\) is the distance of the particle from the center of the field. For stable equilibrium, the distance of the particle is:
1. \(B/A\)
2. \(B/2A\)
3. \(2A/B\)
4. \(A/B\)