Question

In gravity free space, a particle of mass $m$ is attached to a long ideal string. Another end of the string is joined to a vertical cylinder fixed on a smooth horizontal plane as shown in the figure. The particle is projected with speed $u$ in a direction perpendicular to the string. The particle continues to move on a spiral path of decreasing radius. As the particle proceeds on the spiral path, how will the tension in the string and speed of the particle change?

• A. Both will remain constant
• B. Both will increase
• C. Tension will decrease and speed will increase
• D. Tension will increase and speed will remain constant

Answer 1

The correct option is B Both will increase

As particle is moving in gravity free space, hence only force acting on the particle will be tension and centrifugal force.

Tension in the string is $T=m{v}^2/r$.......(1)

As no external torque is acting on the system hence angular momentum of the system will be conserved.

, $\therefore v_1{r}_1=v_2{r}_2$

So, velocity increases as $r$ decreases.

Also, from equation(1) the tension increases as $r$ decreases and $v$ increases.

So, both tension and velocity will increase.