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9
MCQ (Single Correct Answer)

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

A
$$\frac{m v}{2}$$ eastward and is exerted by the car engine
B
$$\frac{m v}{2}$$ eastward and is due to the friction on the tyres exerted by the road
C
more than $$\frac{m v}{2}$$ eastward exerted due to the engine and overcomes the friction of the road
D
$$\frac{m v}{2}$$ exerted by the engine
10
MCQ (Multiple Correct Answer)

The motion of a particle of mass $$m$$ is given by $$x=0$$ for $$t<0$$ s, $$x(t)=A \sin 4 \pi t$$ for $$00)$$, and $$x=0$$ for $$t>(1 / 4) \mathrm{s}$$. Which of the following statements is true?

A
The force at $$t=(1 / 8)$$ s on the particle is $$-16 \pi^2 \mathrm{~A}-\mathrm{m}$$
B
The particle is acted upon by on impulse of magnitude $$4 \pi^2 \mathrm{~A}-\mathrm{m}$$ at $$t=0 \mathrm{~s}$$ and $$t=(1 / 4) \mathrm{s}$$
C
The particle is not acted upon by any force
D
The particle is not acted upon by a constant force
E
There is no impulse acting on the particle
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
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