Question

Two blocks $A$ and $B$ of mass $5\text{kg}$ and $2\text{kg}$, respectively, connected by a spring of force constant $=100\text{N/m}$ and are placed on an inclined plane of inclination ${30}^{\circ }$ as shown. If the system is released from rest then

• A. There will be no compression or elongation in the spring, if all the surfaces are smooth.
• B. There will be elongation in the spring, if $A$ is rough and $B$ is smooth.
• C. Maximum elongation in the spring is $35\text{cm}$, if all surfaces are smooth.
• D. There will be elongation in the spring, if $A$ is smooth and $B$ is rough.

Answer 1

Answer: (A), (D)

The correct options are
A There will be no compression or elongation in the spring, if all the surfaces are smooth.
D There will be elongation in the spring, if $A$ is smooth and $B$ is rough.

When all surfaces are smooth,
acceleration of both blocks is $g\sin \theta$. So, no elongation or compression of spring takes place.

When A is rough, B is smooth,
Acceleration of A < Acceleration of B
Hence, A moves less distance compared to B, and spring will compress.

When B is rough, A is smooth,
Acceleration of B < Acceleration of A
Hence, B moves less distance compared to A, and spring will elongate.

a,d are correct.