Physics, asked by Smtbhd32, 1 year ago

Two masses m and 2m are connected by a string passing over a pulley fixed at the top of an inclined plane.
The first mass moves vertically downwards drawing the second up the incline. If the angle of inclination is e
and the coefficient of friction is u, the acceleration of the system is, less than it would be if the plane were
rough by an amount:​

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Answers

Answered by sonuvuce
55

Answer:

Option (4) \frac{2}{3}\mu g\cos\theta

Explanation:

Let the tension in the string be T

The mass m moves vertically downwards

if the acceleration is a

mg - T = ma      ............ (1)

The block of mass 2m will move with an acceleration a, up the inclined plane

The friction force μN will act opposite its motion i.e. down the inclined plane

N = 2mgcosθ

T - 2mgsinθ - μN = 2ma  

T - 2mgsinθ - 2μmgcosθ = 2ma   .......... (2)

Adding equation (1) and (2)

mg - 2mgsinθ - 2μmgcosθ =3ma

or, a = [1 - 2(sinθ + μcosθ)]g/3

if the plane were not rough then μ = 0

the acceleration will be

A = (1 - 2sinθ)(g/3)

Difference is

A-a=\frac{2}{3}\mu g\cos\theta

Therefore, the acceleration of the system will be less than an amount of \frac{2}{3}\mu g\cos\theta if plane is rough than it would be if plane was smooth

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Answered by vinnu81
3

Sorry ....i could not draw the diagram...Hope it helps you

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