Two masses m and 2m are connected by a light | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Using the principle of conservation of mechanical energy,the loss in potential energy of the $2m$ mass equals the gain in kinetic energy of the sy

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Using the principle of conservation of mechanical energy,the loss in potential energy of the $2m$ mass equals the gain in kinetic energy of the system.Loss in potential energy of $2m$ mass = $(2m)gh$.Gain in potential energy of $m$ mass = $mgh$.Net loss in potential energy = $(2m)gh - mgh = mgh$.This energy is converted into the kinetic energy of the two masses and the rotational kinetic energy of the pulley.Total kinetic energy = $K_{m} + K_{2m} + K_{pulley} = \frac{1}{2}mv^2 + \frac{1}{2}(2m)v^2 + \frac{1}{2}I\omega^2$.Since $I = \frac{1}{2}Mr^2 = \frac{1}{2}(30m)r^2 = 15mr^2$ and $\omega = \frac{v}{r}$,we have $K_{pulley} = \frac{1}{2}(15mr^2)(\frac{v^2}{r^2}) = 7.5mv^2$.Equating energy: $mgh = \frac{1}{2}mv^2 + mv^2 + 7.5mv^2 = 9mv^2$.$v^2 = \frac{gh}{9} = \frac{10 	imes 3.6}{9} = 4$.$v = 2 \ m/s$.

Similar Questions

$A$ mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder,then with what acceleration will the mass be released? (Assume $g =$ acceleration due to gravity)

Two masses $400 \ g$ and $350 \ g$ are suspended from the ends of a light string passing over a heavy pulley of radius $2 \ cm$. When released from rest,the heavier mass is observed to fall $81 \ cm$ in $9 \ s$. The rotational inertia of the pulley is . . . . . . $kg \cdot m^2$. $(g = 9.8 \ m/s^2)$

In the given figure,a solid cylinder of mass $m_2$ and radius $R$ is suspended by a string wrapped around it,which passes over a fixed pulley of mass $m_1$ and radius $R$. If the linear acceleration of the solid cylinder is $a_2$ and there is no slipping,what is its angular acceleration $\alpha_2$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module