# 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: 1. $$mv/2$$ eastward and is exerted by the car engine. 2. $$mv/2$$ eastward and is due to the friction on the tires exerted by the road. 3. more than $$mv/2$$ eastward exerted due to the engine and overcomes the friction of the road. 4. $$mv/2$$ exerted by the engine.

Subtopic:  Newton's Laws | Application of Laws |
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The motion of a particle of mass $$m$$ is given by $$x=0$$ for $$t<0 ~\text s$$, $$x(t)=A~\text {sin}~4\pi t$$ for $$0<t<(1/4) \text s ~(A>0)$$, and $$x=0$$ for $$t>(1/4) ~\text s$$. Then:

 (a) The force at $$t=(1/8) ~\text s$$ on the particle is $$-16 \pi^2\text{Am}$$ (b) The particle is acted upon by an impulse of magnitude $$4 \pi^2 \text{Am}$$ at $$t=0 ~\text s$$ and $$t=(1/4) ~\text s$$ (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

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

 1 (a, c, d, e) 2 (a, c) 3 (b, c, d) 4 (a, b, d)
Subtopic:  Newton's Laws | Application of Laws |
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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 $$rn/2$$ and of $$B$$ is $$m.$$

 (a) The bodies will move together if $$F = 0.25\text{mg}$$ (b) The $$A$$ will slip with $$B$$ if $$F = 0.5\text{mg}$$ (c) The bodies will move together if $$F = 0.5\text{mg}$$ (d) The bodies will be at rest if $$F = 0.1\text{mg}$$ (e) The maximum value of $$F$$ for which the two bodies will move together is $$0.45\text{mg}$$

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)

Subtopic:  Application of Laws | Friction |
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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)​​​​​​​

Subtopic:  Friction |
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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.

 (a) A will never move up the plane (b) A will just start moving up the plane when $$\mu = \frac{{\sin} \left(\theta\right)_{2} - {\sin} \left(\theta\right)_{1}}{{\cos} \left(\theta\right)_{1}}$$ (c) For $$A$$ to move up the plane, $$\left(\theta\right)_{2}$$ must always be greater than $$\left(\theta\right)_{1}$$ (d) $$B$$ will always slide down with a constant speed

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

 1 (b, c) 2 (c, d) 3 (a, c) 4 (a, d)
Subtopic:  Friction |
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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) $$1~\text{ms}^{-2}$$ at an angle of $$\text {tan}^{-1} \left(\dfrac{4}{3}\right )$$ w.r.t. $$6$$ N force (b) $$0.2~\text{ms}^{-2}$$ at an angle of $$\text {tan}^{-1} \left(\dfrac{3}{4}\right )$$ w.r.t. $$8$$ N force (c) $$1~\text{ms}^{-2}$$ at an angle of $$\text {tan}^{-1} \left(\dfrac{3}{4}\right )$$ w.r.t. $$8$$ N force (d) $$0.2~\text{ms}^{-2}$$ at an angle of $$\text {tan}^{-1} \left(\dfrac{3}{4}\right )$$ w.r.t. $$6$$ N force

Choose the correct option:
1. (a), (c)
2. (b), (c)
3. (c), (d)
4. (a), (b), (c)
Subtopic:  Application of Laws |
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A body with a mass of $$5$$ kg is acted upon by a force $$\vec{F}=\left ( -3\hat{i} +4\hat{j}\right )$$ N. If its initial velocity at $$t=0$$ is $$\vec{v}=\left ( 6\hat{i} -12\hat{j}\right )$$ 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

Subtopic:  Newton's Laws |
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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

1. $$136~\text{N}$$
2. $$134~\text{N}$$
3. $$158~\text{N}$$
4. $$68~\text{N}$$
Subtopic:  Newton's Laws | Application of Laws |
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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:

 1 frictional force along westward 2 muscle force along southward 3 frictional force along south-West 4 muscle force a south-West

Subtopic:  Newton's Laws | Application of Laws |
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Conservation of momentum in a collision between particles can be understood from:

 1 conservation of energy 2 newton's first law only 3 newton's second law only 4 both Newton's second and third law
Subtopic:  Newton's Laws | Application of Laws |
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