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11
MCQ (Multiple Correct Answer)

In figure the coefficient of friction between the floor and the body $$B$$ is 0.1. The coefficient of friction between the bodies $$B$$ and $$A$$ is 0.2. A force F is applied as shown on $$B$$. The mass of $$A$$ is $$\mathrm{m} / 2$$ and of $$B$$ is $$m$$. Which of the following statements are true?

A
The bodies will move together if $$\mathbf{F}=0.25 \mathrm{mg}$$
B
The body $$A$$ will slip with respect to $$B$$ if $$\mathbf{F}=0.5 \mathrm{mg}$$
C
The bodies will move together if $$\mathbf{F}=0.5 \mathrm{mg}$$
D
The bodies will be at rest if $$\mathbf{F}=0.1 \mathrm{mg}$$
E
The maximum value of $$\mathbf{F}$$ for which the two bodies will move together is 0.45 mg
12
MCQ (Multiple Correct Answer)

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 figure. The coefficient of friction between $$m_1$$ and the sloping surface is $$\mu$$. Which of the following statements are true?

A
$$ \text { If } m_2>m_1 \sin \theta \text {, the body will move up the plane } $$
B
$$ \text { If } m_2>m_1(\sin \theta+\mu \cos \theta) \text {, the body will move up the plane } $$
C
$$ \text { If } m_2< m_1(\sin \theta+\mu \cos \theta) \text {, the body will move up the plane } $$
D
$$ \text { If } m_2< m_1(\sin \theta-\mu \cos \theta) \text {, the body will move down the plane } $$
13
MCQ (Multiple Correct Answer)

In figure a body $$A$$ of mass $$m$$ slides on plane inclined at angle $$\theta_1$$ 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 $$\theta_2$$ to the horizontal. Which of the following statements are true?

A
A will never move up the plane
B
A will just start moving up the plane when $$ \mu=\frac{\sin \theta_2-\sin \theta_1}{\cos \theta_1} $$
C
For A to move up the plane, $$\theta_2$$ must always be greater than $$\theta_1$$
D
B will always slide down with constant speed
14
MCQ (Multiple Correct Answer)

Two billiard balls $$A$$ and $$B$$, each of mass 50 g and moving in opposite directions with speed of $$5 \mathrm{~m} \mathrm{~s}^{-1}$$ each, collide and rebound with the same speed. If the collision lasts for $$10^{-3} \mathrm{~s}$$, which of the following statements are true?

A
The impulse imparted to each ball is $$0.25 \mathrm{~kg}-\mathrm{ms}^{-1}$$ and the force on each ball is 250 N
B
The impulse imparted to each ball is $$0.25 \mathrm{~kg}-\mathrm{m} \mathrm{s}^{-1}$$ and the force exerted on each ball is $$25 \times 10^{-5} \mathrm{~N}$$
C
The impulse imparted to each ball is $$0.5 \mathrm{~N}-\mathrm{s}$$
D
The impulse and the force on each ball are equal in magnitude and opposite in directions
15
MCQ (Multiple Correct Answer)

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

A
$$1 \mathrm{~m} \mathrm{~s}^{-2}$$ at an angle of $$\tan ^{-1}\left(\frac{4}{3}\right)$$ w.r.t. 6 N force
B
$$0.2 \mathrm{~m} \mathrm{~s}^{-2}$$ at an angle of $$\tan ^{-1}\left(\frac{4}{3}\right)$$ w.r.t. 6 N force
C
$$1 \mathrm{~m} \mathrm{~s}^{-2}$$ at an angle of $$\tan ^{-1}\left(\frac{3}{4}\right)$$ w.r.t. 8 N force
D
$$0.2 \mathrm{~m} \mathrm{~s}^{-2}$$ at an angle of $$\tan ^{-1}\left(\frac{3}{4}\right)$$ w.r.t. 8 N force
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