Q. 12

# Mass m_{1} moves on a slope making an angle θ with the horizontal and is attached to mass m_{2} by a string passing over a frictionless pulley as shown in Fig. 5.2. The co-efficient of friction between m_{1} and the sloping surface is μ. Which of the following statements are true?

A. If m_{2} > m_{2} sin θ, the body will move up the plane.

B. If m_{2} > m_{1} (sinθ + μ cos θ), the body will move up the plane.

C. If m_{2} > m_{1} (sinθ + μ cos θ), the body will move up the plane.

D. If m_{2} > m_{1} (sinθ + μ cos θ), the body will move down the plane.

Answer :

Let’s consider a case in which normal reaction i.e.

N from figure also we know friction

Now from figure taking whole as a system then

when m_{1} will up and m_{2} will down.

Putting f in this equation

⇒

⇒ or in simply

⇒ from this option (a) is totally wrong while option (b) is correct.

Now if body m_{1} moves down and m_{2} moves up then, direction of friction force (f) becomes upward (opp. to motion).

⇒

⇒

⇒

Hence option (d) is correct but option (c) is wrong.

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PREVIOUSIn Fig. 5.1, the co-efficient of friction between the floor and the body B is 0.1. The co-efficient 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 m/2 and of B is m. Which of the following statements are true?NEXTIn Fig. 5.3, a body A of mass m slides on plane inclined at angle θ1 to the horizontal and μ1 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 angle θ2 to the horizontal. Which of the following statements are true?

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