Question

Figure shows a top view of a fixed vertical cyclinder of radius $R$ resting on a horizontal plane. A particle is attached to the cyclinder by a horizontal thread $AB$. The particle is initially at rest on the horizontal plane. A horizontal velocity $V_o$ is imparted to the particle, normal to the thread.
During subsequent motion, which of the following statement(s) are false:

• A. Angular momentum of particle about $O$ remains constant.
• B. Angular momentum of particle about $B$ remains constant.
• C. Linear momentum of particle about $B$ remains constant.
• D. Kinetic energy of the ball remains constant.

Answer 1

Answer: (A), (B), (C)

Linear momentum of particle about $B$ remains constant.


For the particle $N=mg$ [at all point of time]. Their resultant is zero.
Hence, Tension ($T$) is the only force acting on the particle.

Line of action of $T$ passes through $B$ only at the initial instant.
So, $({\tau }_{net}{)}_{aboutB}\ne 0$
So, option ($b$) is incorrect.

About point $O$, $T$ always produces a moment.
$({\tau }_{net}{)}_O=T\times R\ne 0$
Hence, option ($a$) is incorrect.

Also, $\left(F_{net}\right)=T\ne 0$
So, Linear momentum of the particle is not conserned.
Hence option($c$) is incorrect.

However, neither $W_{ext}$ is done on the particlee, nor any energy is lost against friction.
So, the KE of particle remains constant. Option ($d$) is a correct statement.

Hence, the correct answer is ($a$), ($b$) and ($c$).