Physics - Rotation Question with Solution | TestHub

PhysicsRotationTorque / angular accelerationMedium2 minQB

PhysicsMediumnumerical

Passage / Comprehension

There is a rod of length ' $ℓ$ ', mass ' $m$ ' lying on a horizontal table. An ideal cord is led through a pulley (ideal) and its horizontal part is attached to one end A of the rod, while its vertical part is attached to a weight of mass $m_{1}$ . There is no friction on table or pulley.\\

By changing mass ratio $\frac{m}{m _{1}}$ , the acceleration of the centre of the rod at the moment of releasing the weight changes. What is the maximum possible acceleration of centre of rod? Mark the acceleration divided by acceleration due to gravity.

Answer:

0.25

Solution:

From Q1: $a_{A} = 4 a_{0}$ (acceleration of end A = acceleration of the cord and weight).

$m_{1} g - T = m_{1} a_{A}; T = m a_{0} \Rightarrow m_{1} g - m a_{0} = 4 m_{1} a_{0} \Rightarrow a_{0} = \frac{g}{\frac{m}{m _{1}} + 4}$

Maximum as $\frac{m}{m _{1}} \to 0$ : $a_{0} \to \frac{g}{4} \Rightarrow \frac{a _{0}}{g} = 0.25$

Stream:JEESubject:PhysicsTopic:RotationSubtopic:Torque / angular acceleration

⏱ 2mℹ️ Source: QB

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