Two block A and B of equal mass are connected using a light inextensible string passing over two light smooth pulleys fixed to the blocks (see fig). The horizontal surface is smooth. Every segment of the string (that is not touching the pulley) is horizontal. When a horizontal force F1 is applied to A the magnitude of momentum of the system, comprising of A + B, changes at a rate R. When a horizontal force F2 is applied to B (F1 not applied) the magnitude of momentum of the system A + B once again changes at the rate R. Which force is larger- F1 or F2?

Rate of change of momentum = Net external force. External forces are (F1 or F2) and the force applied by the support on the string. When F1 is applied, the support exerts a force (T1) on the string in the direction of F1 ∴R=F1+T1 ………….1When F2 is applied R=F2−T2 ……………..2[T2 = force by the support on the string] From 1 and 2 F2- F1 = T1+T2 >0∴F2>F1

Two block A and B of equal mass are connected using a light inextensible string passing over two light smooth pulleys fixed to the blocks (see fig). The horizontal surface is smooth. Every segment of the string (that is not touching the pulley) is horizontal. When a horizontal force F1 is applied to A the magnitude of momentum of the system, comprising of A + B, changes at a rate R. When a horizontal force F2 is applied to B (F1 not applied) the magnitude of momentum of the system A + B once again changes at the rate R. Which force is larger- F1 or F2?

Rate of change of momentum = Net external force. External forces are (F1 or F2) and the force applied by the support on the string. When F1 is applied, the support exerts a force (T1) on the string in the direction of F1 ∴R=F1+T1 ………….1When F2 is applied R=F2−T2 ……………..2[T2 = force by the support on the string] From 1 and 2 F2- F1 = T1+T2 >0∴F2>F1

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Two block A and B of equal mass are connected using a light inextensible string passing over two light smooth pulleys fixed to the blocks (see fig).
The horizontal surface is smooth. Every segment of the string (that is not touching the pulley) is horizontal. When a horizontal force F₁ is applied
to A the magnitude of momentum of the system, comprising of A + B, changes at a rate R. When a horizontal force F₂ is applied to B (F₁ not applied)
the magnitude of momentum of the system A + B once again changes at the rate R. Which force is larger- $F_{1} or F_{2} ?$

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$F_{1} = F_{2}$

$F_{2} < F_{1}$

From the given relation it is not possible to find the relation between $F_{1} a n d F_{2} .$

$F_{2} > F_{1}$

answer is C.

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Detailed Solution

Rate of change of momentum = Net external force. External forces are (F₁ or F₂) and the force applied by the support on the string. When F1 is applied, the support exerts a force (T₁) on the string in the direction of F₁

$∴ R = F_{1} + T_{1}$ …………. $(1)$
When F₂is applied
$R = F_{2} - T_{2}$ …………….. $(2)$
[T₂ = force by the support on the string]