Question

A body of mass $M$ is made to revolve along a circle of radius $r$ in a horizontal plane at a speed of $vm/s$ with the help of light horizontal string such that the tension in the string is $10N$. Keeping the speed constant, if the mass is increased to $2M$ and radius is decreased to $\frac{r}{2}$, then tension in the string is:

• A. $10N$
• B. $20N$
• C. $40N$
• D. $5N$

Answer 1

The correct option is C $40N$

We know, $T=$ Tension $=\frac{M{v}^2}{r}$
So, $T\propto \frac{M}{r}$

$\Rightarrow$$\frac{T_1}{T_2}=\frac{M_1}{r_1}\times \frac{r_2}{M_2}$

or, $\frac{T_1}{T_2}=\frac{M_1}{M_2}\times \frac{r_2}{r_1}$

or, $\frac{10}{T_2}=\frac{M}{2M}\times \frac{r}{2r}=\frac{1}{4}$

or, $T_2=40N$