Question

Two metallic cylinder made of same material and radii $r$ and $2r$ are joined as shown in figure. If top end is fixed and lower end of cylinder $B$ is twisted by angle $\theta$, then angle of twist for cylinder $A$ is (both cylinder have same length).

• A. $\frac{15}{16}\theta$
• B. $\frac{16}{15}\theta$
• C. $17\theta$
• D. $\frac{16}{17}\theta$

Answer 1

The correct option is D $\frac{16}{17}\theta$

The correct option is D

Given,

Two cylinder having $radii=r,2r$

Let the total angle twisted is A and B.

Now,

The force applied to produce the torque on B and a restoring torque is

produce in A to counter torque of B.

This continued till both the rods does not archive the conditions of equilibrium.

Using the formula of torque in both cylinder A and B

Torque clockwise by B =torque clockwise by A

$n\times \pi \left(2r\right)4\theta \frac{2}{2L}=n\times \pi \left(r\right)4\theta \frac{1}{L}$

${\theta }_1=16{\theta }_2$

Therefore,

${\theta }_2=\frac{16\theta }{17}$