A particle of mass \(M\) starting from rest undergoes uniform acceleration. If the speed acquired in time \(T\) is \(V\), the power delivered to the particle is:
1. \(\frac{1}{2}\frac{MV^2}{T^2}\)
2. \(\frac{MV^2}{T^2}\)
3. \(\frac{1}{2}\frac{MV^2}{T}\)
4. \(\frac{MV^2}{T}\)
A stone is dropped from a height \(h\). It hits the ground with a certain momentum \(p\). If the same stone is dropped from a height \(100\)% more than the previous height, the momentum when it hits the ground will change by:
1. \(41\)%
2. \(200\)%
3. \(100\)%
4. \(68\)%
A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude \(P_0\). The instantaneous velocity of this car is proportional to:
1. \(t^{\frac{1}{2}}\)
2. \(t^{\frac{-1}{2}}\)
3. \(\frac{t}{\sqrt{m}}\)
4. \(t^2 P_0\)
A mass \(m\) moving horizontally (along the x-axis) with velocity \(v\) collides and sticks to a mass of \(3m\) moving vertically upward (along the y-axis) with velocity \(2v.\) The final velocity of the combination is:
1. \(\frac{3}{2}v\hat{i}+\frac{1}{4}v\hat{j}\)
2. \(\frac{1}{4}v\hat{i}+\frac{3}{2}v\hat{j}\)
3. \(\frac{1}{3}v\hat{i}+\frac{2}{3}v\hat{j}\)
4. \(\frac{2}{3}v\hat{i}+\frac{1}{3}v\hat{j}\)
If , then work done in the first 4s will be:
(Mass of the particle is 3 gram)
1. 384 mJ
2. 168 mJ
3. 192 mJ
4. None of the above
Two identical balls A and B are moving with velocity and respectively. If they collide head on elastically, then their velocities after collision will be:
1.
2.
3.
4.
A bomb of mass 30kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18kg mass is 6ms–1. The kinetic energy of the other mass is:
1. 524 J
2. 256 J
3. 486 J
4. 324 J
The bob of a simple pendulum having length l, is displaced from the mean position to an angular position θ with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:
1.
2.
3.
4.
If \(\vec{F} = (60\hat{i} + 15\hat{j}-3\hat{k})\) N and \(\vec{v} = (2\hat{i} - 4\hat{j}+5\hat{k})\) m/s, then instantaneous power is:
1. \(195\) watt
2. \(45\) watt
3. \(75\) watt
4. \(100\) watt
A ball is dropped from a height of \(5\) m. If it rebounds up to a height of \(1.8\) m, then the ratio of velocities of the ball after and before the rebound will be:
1.
2.
3.
4.