Question

In $Fig.$, blocks A and B move with velocities $v_1$ and $v_2$ along horizontal direction. Find the ratio of $v_1/v_2$.

• A. $\frac{\sin {\theta }_1}{\sin {\theta }_2}$
• B. $\frac{\sin {\theta }_2}{\sin {\theta }_1}$
• C. $\frac{\cos {\theta }_2}{\cos {\theta }_1}$
• D. $\frac{\cos {\theta }_1}{\cos {\theta }_2}$

Answer 1

The correct option is C $\frac{\cos {\theta }_2}{\cos {\theta }_1}$

By using the law of constrained motion

The amount by which the string attached to A moves$\left(d{s}_1\right)$=The amount by which the string attached to B moves $\left(d{s}_2\right)$

As they are part of the same string

Therefore components of velocities of A and B along the strings are equal

So, $v_1\cos {\theta }_1=v_2\cos {\theta }_2$

$\therefore \frac{v_1}{v_2}=\frac{\cos {\theta }_2}{\cos {\theta }_1}$