Question

In the above figure, all surfaces are assumed to be frictionless and pulley is assumed to be ideal. The block 'A' is projected towards the pulley 'P' with an initial velocity $u_0$. Which of the following is/are incorrect?

• A. The string would become tight at $t=\frac{2u_0}{g}$
• B. The distance travelled by 'A' before the string is taut is $\frac{u_0^2}{g}$
• C. The distance travelled by 'B' before string is taut is $\frac{2u_0^2}{g}$
• D. The common speed of the blocks just after the string is taut is $\left(\frac{n+2}{n+1}\right)u_0$

Answer 1

The correct option is B The distance travelled by 'A' before the string is taut is $\frac{u_0^2}{g}$

When the string is taut again both blocks will travel same distance.

As B falling free, $u_{0}t=\frac{1}{2}g{t}^2$ , $t=\frac{2u_0}{g}$

Distance travel by A and B block $=u_{0}t=\frac{2u_0^2}{g}$

Also when same impulse acts along the wire the change in
momentum would be same for both blocks.

$J=nmv-nm{u}_0$ (for block A)

$-J=mv-m\left(2u_0\right)$ (for block B)

$\therefore nmv-nm{u}_0=2m{u}_0-mv$

$(n+1)v=(n+2)u_0$

$v=\left(\frac{n+2}{n+1}\right)u_0$