A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :

Question

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is : (A) (2 mg/ 2 m + M ) (B) (2 Mg/ 2 m + M ) (C) (2 mg/ 2 M + m ) (D) (2 Mg/ 2 M + m )

Tardigrade Admin · Accepted Answer

mg - T = ma RT = I propto RT = (MR2/2). (a/R) T = (Ma/2) mg - (Ma/2) = ma mg - a((M/2)+m) mg - a((M+2m/2)) a = (2mg/M+2m)

Q. A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :

$\frac{2 m g}{2 m + M}$

$\frac{2 M g}{2 m + M}$

$\frac{2 m g}{2 M + m}$

$\frac{2 M g}{2 M + m}$

$m g - T = ma$
$RT = I \propto$
$RT = \frac{M R ^{2}}{2} . \frac{a}{R}$
$T = \frac{M a}{2}$
$m g - \frac{M a}{2} = ma$
$m g - a (\frac{M}{2} + m)$
$m g - a (\frac{M + 2 m}{2})$
$a = \frac{2 m g}{M + 2 m}$

Q. A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :

2m+M2mg​

2m+M2Mg​

2M+m2mg​

2M+m2Mg​

mg−T=ma RT=I∝ RT=2MR2​.Ra​ T=2Ma​ mg−2Ma​=ma mg−a(2M​+m) mg−a(2M+2m​) a=M+2m2mg​

$\frac{2 m g}{2 m + M}$

$\frac{2 M g}{2 m + M}$

$\frac{2 m g}{2 M + m}$

$\frac{2 M g}{2 M + m}$

$m g - T = ma$
$RT = I \propto$
$RT = \frac{M R ^{2}}{2} . \frac{a}{R}$
$T = \frac{M a}{2}$
$m g - \frac{M a}{2} = ma$
$m g - a (\frac{M}{2} + m)$
$m g - a (\frac{M + 2 m}{2})$
$a = \frac{2 m g}{M + 2 m}$