A block of mass \(m\) is moving with initial velocity \(u\) towards a stationary spring of stiffness constant \(k\) attached to the wall as shown in the figure. Maximum compression of the spring is:
(The friction between the block and the surface is negligible).
1. | \(u\sqrt{\dfrac{m}{k}}\) | 2. | \(4u\sqrt{\dfrac{m}{k}}\) |
3. | \(2u\sqrt{\dfrac{m}{k}}\) | 4. | \(\dfrac12u\sqrt{\dfrac{k}{m}}\) |
1. | \(W_1=W_2=W_3\) | 2. | \(W_1>W_2>W_3\) |
3. | \(W_1>W_3>W_2\) | 4. | \(W_1<W_2<W_3\) |
Assertion (A): | When a firecracker (rocket) explodes in mid-air, its fragments fly in such a way that they continue moving in the same path, which the firecracker would have followed, had it not exploded. |
Reason (R): | Explosion of cracker (rocket) occurs due to internal forces only and no external force acts for this explosion. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | (A) is false but (R) is true. |
A particle of mass \(4M\) kg at rest splits into two particles of mass \(M\) and \(3M.\) The ratio of the kinetic energies of mass \(M\) and \(3M\) would be:
1. | \(3:1\) | 2. | \(1:4\) |
3. | \(1:1\) | 4. | \(1:3\) |
1. | \(23500\) | 2. | \(23000\) |
3. | \(20000\) | 4. | \(34500\) |
1. | \(16U\) | 2. | \(2U\) |
3. | \(4U\) | 4. | \(8U\) |