Question 332: Centre of Mass and Rotational Motion

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 :

Accepted Answer

From figure, we can say
ma = mg $$-$$ T . . . . . (1)
Moment of inertia of a uniform disc,
I = $${1 \over 2}$$ MR
2
and the acceleration of the disc, a = $$ \propto $$ R
We know,
Torque = I$$ \propto $$ = RT
$$	herefore\,\,\,$$  RT = $${1 \over 2}$$ M R
2
$$ 	imes $$ $${a \over R}$$ = $${{MaR} \over 2}$$
$$ \Rightarrow $$ $$\,\,\,$$ T = $${{Ma} \over 2}$$
Putting the value of T in eq (1).
ma = mg $$-$$ $${{Ma} \over 2}$$
$$ \Rightarrow $$ $$\,\,\,$$ a ( m + $${{Ma} \over 2}$$) = mg
$$ \Rightarrow $$ $$\,\,\,$$ a = $${{2mg} \over {2m + M}}$$

Answer

$${{2\,\,mg} \over {2\,m + M}}$$

Answer

$${{2\,\,Mg} \over {2\,m + M}}$$

Answer

$${{2\,\,mg} \over {2\,M + m}}$$

Answer

$${{2\,\,Mg} \over {2\,M + M}}$$

Centre of Mass and Rotational Motion

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 :

Choose the correct answer: