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:
Answers
Answer:
Option (4)
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
Therefore, the acceleration of the system will be less than an amount of if plane is rough than it would be if plane was smooth
Sorry ....i could not draw the diagram...Hope it helps you