Analyze motion of the two bodies connected by string:

Analyze motion of the two bodies connected by string one of which is hanging free and other lying on smooth inclined plane.

Sol.: Consider the two bodies having weight W₁ and W₂ respectively connected by light inextensible string as shown in the figure given below.

Let body W₁ hang free and the W₂ be places on the inclined smooth plane. W₁ will move downwards and body W₂ will move upwards along inclined surface. A little consideration will show that velocity and acceleration of body W₁ will be same as W₂. As the string is inextensible, thus tension in both strings will be equal.

Consider motion of W₁W  - T = (W₁/g)a                                                                                                   ...(1)

Consider motion of W₁

T - W₂ sin ± = (W₁/g)a                                                                                                                               ...(2)

Solve equations for 'T' and 'a'