Question

A smooth ring A of mass m can slide on a fixed horizontal rod A string tied to the ring passes over a fixed pulley B and carries a block C of mass 2m as shown in figure.At the instant the string between the ring and the ring and the pulley makes an ngle $\theta$ with the rod. With what acceleration will the ring start if the moving if the system is released form rest with $\theta ={60}^o$

• A. $\frac{2g}{3}$
• B. $\frac{g}{3}$
• C. $\frac{g}{2}$
• D. $\frac{3g}{2}$

Answer 1

The correct option is B $\frac{g}{3}$

$AD=x,BC=y$

L=length of string-

Length AB at this instant will (l-y)

$\Delta B$ = constant

${\left(l-y\right)}^2=x^2+d^2$

$z\left(l-y\right)\left(\frac{-dy}{dt}\right)=2x\left[\frac{dx}{dt}\right]+0$

$\frac{dy}{dt}=\left(\frac{x}{l-y}\right)\left[\frac{-dx}{dt}\right]$

$\frac{dy}{dt}=$ speed of block C.

$-\frac{dx}{dt}=$ speed of ring A=V,

$\frac{x}{l-y}=\cos \theta$