Mass $m_{1}$ moves on a slope making an angle $\theta$ with the horizontal and is attached to mass $m_{2}$ by a string passing over a frictionless pulley as shown in the figure. The coefficient of friction between $m_{1}$ and the sloping surface is $\mu$.
              

(a)	If $m_{2} > m_{1} \text{sin} ⁡ \theta$, the body will move up the plane.
(b)	If  $m_{2} > m_{1} (\text{sin} ⁡ \theta +\mu \text{cos} \theta)$, the body will move up the plane.
(c)	If  $m_{2} < m_{1} (\text{sin} ⁡ \theta +\mu \text{cos} \theta)$, the body will move up the plane.
(d)	If  $m_{2} < m_{1} (\text{sin} ⁡ \theta -\mu \text{cos} \theta)$, the body will move down the plane.

Which of the following statement/s is/are true?

1.	(a), (d)	2.	(a), (c)
3.	(c), (d)	4.	(b), (d)

In figure a body $A$ of mass $m$ slides on a plane inclined at angle $\left(\theta_{1}\right)$ to the horizontal and $\mu$ is the coefficient of friction between $A$ and the plane. $A$ is connected by a light string passing over a frictionless pulley to another body $B,$ also of mass $m$, sliding on a frictionless plane inclined at an angle $\left(\theta_{2}\right)$ to the horizontal.

Which of the following statement/s is/are true?

A body of mass $10$ kg is acted upon by two perpendicular forces, $6$ N and $8$ N. The resultant acceleration of the body is:

In the figure, the coefficient of friction between the floor and body $B$ is $0.1.$ The coefficient of friction between bodies $B$ and $A$ is $0.2.$ A force $F$ is applied as shown on $B.$ The mass of $A$ is $m/2$ and of $B$ is $m.$

Which of the following statement(s) is/are true?
1. (a), (b), (d), (e)
2. (a), (c), (d), (e)
3. (b), (c), (d)
4. (a), (b), (c)

A car of mass $m$ starts from rest and acquires a velocity along the east, $v=v\mathrm{\hat{i}}(v>0)$ in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is:

A body with a mass of $5$ kg is acted upon by a force $\vec{F}=( -3\hat{i} +4\hat{j})$ N. If its initial velocity at $t=0$ is $\vec{v}= ( 6\hat{i} -12\hat{j} )$ m/s, the time at which it will just have a velocity along the Y-axis is:
1. never
2. $10$ s
3. $2$ s
4. $15$ s

A body of mass $2~\text{kg}$ travels according to the law $x \left( t \right) = pt + qt^2+ rt^3$ where, $p = 3 ~\text{ms }^{−1 },$ $q = 4 ~\text{ms }^{−2}$ and $r = 5 ~\text{ms }^{−3}$. The force acting on the body at $t = 2 ~\text{s }$ is

A hockey player is moving northward and suddenly turns westward at the same speed to avoid an opponent. The force that acts on the player is:

Conservation of momentum in a collision between particles can be understood from:

A cricket ball of mass 150 g has an initial velocity $\small {u = \left(3 \hat{i} + 4 \hat{j} \right) \text {ms}^{- 1}}$ and a  final velocity $\small {v = - \left( 3 \hat{i} + 4 \hat{j} \right) \text{ms}^{- 1}}$, after being hit. The change in momentum (final momentum-initial momentum) is (in kgm/s)
1. $\text {zero}$
2. $-\left ( 0.45\hat{i}+0.6\hat{j} \right )$
3. $-\left ( 0.9\hat{i}+1.2\hat{j} \right )$
4. $-5\left ( \hat{i} +\hat{j}\right )$