Physics - Laws Motion - Quiz-8

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Two blocks of masses 2 kg and 3 kg are tied at the ends of a light inextensible string passing over a frictionless pulley as shown.

If the system is accelerating upward with acceleration $5 m / s^{2}$ , the tension in the string is:

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24 N
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36 N
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48 N
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18 N

A body, under the action of a force $\vec{F} = 6 \hat{i} - 8 \hat{j} + 10 \hat{k}$ , acquires an acceleration of 1 ms^-2. The mass of this body must be:

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2 √10 kg
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10 kg
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20 kg
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10 √2 kg

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between:

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14 m/s and 15 m/s
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15 m/s and 16 m/s
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16 m/s and 17 m/s
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13 m/s and 14 m/s

A block B is pushed momentarily along a horizontal surface with an initial velocity 'v'. If μ is the coefficient of sliding friction between B and the surface, the block B will come to rest after a time:

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$\frac{v}{g μ}$
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$\frac{g μ}{v}$
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$\frac{g}{v}$
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$\frac{v}{g}$

A particle slides down on a smooth incline of inclination

$30^{0}$ , fixed in an elevator going up with an acceleration of 2 m/s². The box of incline has a length of 4 m. The time taken by the particle to reach the bottom will be:

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$\frac{8}{9} \sqrt{3} s$

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$\frac{9}{8} \sqrt{3} s$

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$\frac{4}{3} \sqrt{\frac{\sqrt{3}}{2} s}$

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$\frac{3}{4} \sqrt{\frac{\sqrt{3}}{2} s}$

A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of $30^{o}$ with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25 s, the average force acting on the wall is:

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48 N
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24 N
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12 N
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96 N

A boy on a cycle pedals around a circle of 20 meters radius at a speed of 20 m/s. The combined mass of the body and the cycle makes with the vertical so that it may not fall is (g = 9.8 m/s² )

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60.25 °
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63.90 °
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26.12 °
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30.00 °

A block of mass 10 kg is in contact with the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder, which is vertical and rotating about its axis, will be:
(g=10 m/s²)

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$10 π rad / s$
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$\sqrt{10} π rad / s$
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$\frac{10}{2 π} rad / s$
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$10 rad / s$

A particle moving with velocity $\vec{v}$ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will:

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change according to the smallest force $\vec{Q R}$ .
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increase.
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decrease.
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remain constant.

A mass m₁, placed on top of a trolley of mass m₃, is connected to another mass m₂ by means of string passing over a smooth pulley as shown in figure. The friction between surfaces is negligible. For m₁ ans m₂ not to move with respect to trolley, the horizontal force F to be applied on trolley is

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F=m₃g
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F=(m₁ + m₂)g
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$F = (m_{1} + m_{2} + m_{3}) \frac{m_{2} g}{m_{1}}$
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F= m₁g

A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string when the trolley rolls up a plane of inclination $α$ with acceleration $a_{0}$ is

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$θ = \tan^{- 1} α$
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$θ = \tan^{- 1} (\frac{a_{0}}{g})$
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$θ = \tan^{- 1} (\frac{g}{a_{0}})$
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$θ = \tan^{- 1} (\frac{a_{0} + g \sin α}{g \cos α})$

The pulleys and string shown in the figure are smooth and of negligible mass. For the system of remain in equilibrium, the angle $θ$ should be

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0 $°$
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30 $°$
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45 $°$
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60 $°$

System shown in figure is in equilibrium and at rest. The spring and string are massless, now the stringis cut. The acceleration of mass 2m and m just after string is cut will be

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g/2 upwards, g downwards
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g upwards, g/2 downwards
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g upwards, 2g downwards
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2g upwards, g downwards

A block can slide on a smooth inclined plane of inclination $θ$ kept on the floor of a lift. When the lift is descending with retardation a, the acceleration of the block relative to the incline is:

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(g + a) sin $θ$
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(g – a)
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g sin $θ$
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(g – a) sin $θ$

In the shown system, each of the block is at rest. The value of $θ$ is:

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$\tan^{- 1} (1)$
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$\tan^{- 1} (\frac{3}{4})$
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$\tan^{- 1} (\frac{4}{3})$
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$\tan^{- 1} (\frac{3}{5})$

At a given instant, A is moving with velocity of 5 m/s upwards. What is velocity of B at this time?

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15 m/s $↓$
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15 m/s $↑$
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5 m/s $↓$
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5 m/s $↑$

The blocks A and B are shown in figure have masses 5 kg and 4 kg respectively. The system is released from rest. The speed of B after A has travelled a distance 1 m along the incline is (take g = 10 $m / s^{2}$ , pulleys and strings are ideal and plane is smooth)

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$\sqrt{\frac{5}{6}} m / s$
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$\sqrt{\frac{6}{5}} m / s$
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$\sqrt{\frac{3}{2}} m / s$
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$\sqrt{\frac{2}{3}} m / s$

A truck is stationary and has a bob suspended by a light string in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of a. In the frame of the truck, the pendulum will tilt:

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to the left and angle of inclination of the pendulum with the vertical is $\sin^{- 1} (\frac{a}{g})$
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to the left and angle of inclination of the pendulum with the vertical is $\cos^{- 1} (\frac{a}{g})$
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to the left and angle of inclination of the pendulum with the vertical is $\tan^{- 1} (\frac{a}{g})$
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to the left and angle of inclination of the pendulum with the vertical is $\tan^{- 1} (\frac{g}{a})$

A body of mass m is kept on a rough horizontal surface (coefficient of friction= $μ$ ). A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $\vec{F}$ , where:

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$| \vec{F} | = m g + μ m g$
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$| \vec{F} | = μ m g$
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$| \vec{F} | \leq m g \sqrt{1 + μ^{2}}$
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$| \vec{F} | = m g$

A ladder rests against a smooth vertical wall as shown in the figure. The floor is also smooth. The mass of the ladder is 75 kg. If upper-end A is moving with velocity v vertically downward, then the horizontal velocity of lower end B is :

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v
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$\frac{3}{4} v$
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$\frac{4}{3} v$
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$\frac{3}{5} v$

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