TS EAMCET · Physics · Rotational Motion

Consider two masses $m_{1}$ and $m_{2}$ are connected through a pulley. Mass ' $m_{2}$ ' stats from rest at height ' $h$ ' and falls down. With what speed it hits the ground? (Assume no friction and massless strings & pulleys)

A $\sqrt{(\frac{m_{2}}{m_{1} + m_{2}}) g h}$
B $\sqrt{2 g h}$
C $\sqrt{(\frac{m_{2}}{m_{1} + m_{2}}) 2 g h}$
D $\sqrt{(\frac{m_{1}}{m_{1} + m_{2}}) 2 g h}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\sqrt{(\frac{m_{2}}{m_{1} + m_{2}}) 2 g h}$

Step-by-step Solution

Detailed explanation

In the above diagram, the tension always acted towards pulley now the equations of motion in terms of a tension of the string and acceleration of the block, T=m1a & m2g-T=m2a⇒a=m2gm1+m2 Now calculate the final speed of the particle, v2=0+2ah⇒v=2ah, now…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match the following

	Column-I		Column-II
(A)	Shear modulus	(I)	Resistance to change in volume
(B)	Shearing stress	(II)	Proportionality constant
(C)	Elastic fatigue	(III)	Tangential stress
(D)	Modulus of elasticity	(IV)	Temporary loss of elastic property
		(V)	Resistance to change against deformation force

The correct match is

TS EAMCET 2022 Easy

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Consider two masses m1 and m2 are connected through a pulley. Mass ' m2 ' stats from rest at height ' h ' and falls down. With what speed it hits the ground? (Assume no friction and massless strings & pulleys)

Step-by-step Solution

Consider two masses $m_{1}$ and $m_{2}$ are connected through a pulley. Mass ' $m_{2}$ ' stats from rest at height ' $h$ ' and falls down. With what speed it hits the ground? (Assume no friction and massless strings & pulleys)