When a ball of mass \(5\ \text{kg }\)hits a bat with a velocity \(3\ \text{m/s}\), in the positive direction, and it moves back with a velocity \(4\ \text{m/s}\). The impulse in SI units is:

1. \(5 \)

2. \(15\)

3. \(25\)

4. \(35\)

A bullet of mass \(5 ~\text g\) is fired at a velocity of \(900~\text{ms}^{-1}\) from a rifle of mass \(2.5 ~\text{kg.}\) The recoil velocity of the rifle is:
1. \(0.9~\text{ms}^{-1}\)
2. \(180~\text{ms}^{-1}\)
3. \(900~\text{ms}^{-1}\)
4. \(1.8~\text{ms}^{-1}\)

A lighter body and a heavier body are both moving with the same momentum and are subjected to the same retarding force. Their stopping distances are \(s_1\) and \(s_2\) respectively. Then the correct relation between ${}_{}$ \(s_1\) and \(s_2\)  is:

1. \(s_1 >s_2\)

2. \(s_1<s_2\)

3. \(s_1=s_2\)

4. None of these

A metal ring of mass \(m\) and radius \(R\) is placed on a smooth horizontal table and is set to rotate about its own axis in such a way that each part of the ring moves with a speed \(v\).
  
The tension in the ring is:

1. \(\dfrac{mv^2}{R}\)
2. \(\dfrac{mv^2}{2R}\)
3. \(\dfrac{mv^2}{2\pi R}\)
4. \(\text{None of these}~\)

While walking on ice, one should take small steps to avoid slipping. This is because smaller steps ensure:

1. Larger friction
2. Smaller friction
3. Larger normal force
4. Smaller normal force

A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it:

1.  Increases

2.  decreases

3.  remains the same

4.  fluctuates erratically

Two blocks A and B of masses m & 2m respectively are held at rest such that the spring is in natural length. Find the accelerations of both the blocks just after release.

1. \(g \downarrow ,   g \downarrow\)

2. \(\frac{g}{3} \downarrow ,   \frac{g}{3} \uparrow\)

3. (0, 0)

4. \(g \downarrow ,   0\)

Five persons \(A,\ B,\ C,\ D\ \text{and}\ E \) are pulling a cart of mass \(100\ \text{kg}\) on a smooth surface, and the cart is moving with an acceleration \(3 \ \text{m /s} ^ 2\) in the East direction. When person \(A\) stops pulling, it moves with an acceleration \(1 \ \text{m /s}^ 2\) in the west direction. When person\(​​B\) stops pulling, it moves with an acceleration \(24 \ \text{m/s}^ 2\) in the north direction. The magnitude of the acceleration of the cart when only \(A\) and\(​​B\) pull the cart, keeping their directions the same as the old directions, is:

1. \(26 \ \text{m/s}^ 2\)
2. \(3\sqrt{71} \ \text{m/s}^ 2\) $\mathrm{}$
3. \(25 \ \text{m/s}^ 2\)
4. \(30 \ \text{m/s}^ 2\)

A body moves along an uneven surface with constant speed at all points. The normal reaction due to ground on the body is: