Question

Two blocks are connected with a string and the system is connected to another string which is fixed at the centre of a circular table as shown in the figure. The table is rotating with an angular speed of $\omega$ about its centre. Find the tension in the string which is fixed at the centre.

• A. $m{\omega }^2{r}_1$
• B. $m{\omega }^2{r}_2$
• C. $m{\omega }^2(r_1+r_2)$
• D. $m{\omega }^2(r_1-r_2)$

Answer 1

The correct option is C $m{\omega }^2(r_1+r_2)$

The free body diagram of the system can be shown as below.


Applying Newton's 2nd law for block 1
$T_1-T_2=m{\omega }^2{r}_1.......\left(i\right)$
Applying Newton's 2nd law for block 2
$T_2=m{\omega }^2{r}_2.......\left(ii\right)$
Adding equation $\left(i\right)$ and $\left(ii\right)$
$T_1=m{\omega }^2(r_1+r_2)$