A ball of mass \(100~\text g\) is released from a height of \(10 ~\text{m}\) above the ground. After striking the ground, it rebounds to a height of \(5 ~\text{m}.\) The magnitude of the impulse imparted to the ball by the ground is: \((g=10~\text{m/s}^2 )\)
1. \((\sqrt2-1)~\text{N-s}\)
2. \((\sqrt2+2)~\text{N-s}\)
3. \((2\sqrt2-1)~\text{N-s } \)
4. \((\sqrt2+1)~\text{N-s } \)

| 1. | \(\dfrac{M_2}{M_1}\) | 2. | \(\dfrac{M_1+M_2}{M_1}\) |
| 3. | \(\dfrac{M_1+M_2}{M_2}\) | 4. | \(\dfrac{M_1}{M_1+M_2}\) |
| 1. | \( \dfrac{9}{7}\) | 2. | \(\dfrac{8}{7}\) |
| 3. | \(\dfrac{5}{7}\) | 4. | \( \dfrac{9}{8}\) |

A particle of mass \(500~\text{g}\) is moving with a velocity given by:
\(\vec{v}=(2 t \hat{i}+3 t^2 \hat{j})~ \text{m} / \text{s}.\)
If the force acting on the particle at \(t=1~\text{s}\) is \(\vec{F}=( \hat{i}+x \hat{j})~ \text{N},\) then the value of \(x\) is:
| 1. | \(6\) | 2. | \(1\) |
| 3. | \(2\) | 4. | \(3\) |