162. The velocity of a 2kg ball changes from $\vec{V}_1 = 10\hat{i} - 8\hat{j}$ to $\vec{V}_2 = 6\hat{i} - 5\hat{j}$ (in SI units) under a constant force. If the time of force application is $\frac{1}{10}$ seconds, the magnitude of the force is how many Newtons?
(1) $10$ (2) $12$ (3) $15$ (4) $20$

164- The magnitude of motion (momentum) of a body with mass 2 kg is $6\,\dfrac{\text{kg}\cdot\text{m}}{\text{s}}$. What is the kinetic energy of the body in joules?
(1) $3$ (2) $6$ (3) $9$ (4) $12$

183. A projectile of mass $m$ with initial speed $V_\circ$ is launched at angle $\alpha$ to the horizontal and reaches the ground after $2t$ seconds. What is the magnitude of the change in momentum of the projectile during the first $t$ seconds of motion? (Neglect air resistance.)
$$2mgt \quad (1) \qquad mgt \quad (2) \qquad \dfrac{mv_\circ}{2} \quad (3) \qquad \dfrac{2mv_\circ}{2} \quad (4)$$
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STATEMENT-1
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. because STATEMENT-2 In an elastic collision, the linear momentum of the system is conserved.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True

A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of $45^{\circ}$ with the initial vertical direction is
(1) $Mg(\sqrt{2} - 1)$
(2) $Mg(\sqrt{2} + 1)$
(3) $Mg\sqrt{2}$
(4) $\frac{Mg}{\sqrt{2}}$

The figure shows the position-time $(x-t)$ graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is
(1) 0.4 Ns
(2) 0.8 Ns
(3) 1.6 Ns
(4) 0.2 Ns

A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre?

A body of mass 5 kg moving with a uniform speed $3 \sqrt { 2 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in $X - Y$ plane along the line $y = x + 4$. The angular momentum of the particle about the origin will be $\_\_\_\_$ $\mathrm { kg } \mathrm { m } ^ { 2 } \mathrm {~s} ^ { - 1 }$.