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Question

Three forces are acting on a particle of mass m initially in equilibrium. If the first two forces (R1 and R2) are perpendicular to each other and suddenly the third force (R3) is removed, then the acceleration of the particle is

A
R3m
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B
R1+R2m
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C
R1R2m
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D
R1m
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Solution

The correct option is A R3m

Given,

Magnitude of Forces on object are R1, R2&R3

Two forces R1 & R2 are normal to each other.

In vector form R1, R2&R3.

Two forces R1 & R2 are normal to each other.

Initially object is in equilibrium, mean vector sum of forces is zero.

R1+ R2+R3=0 (at equilibrium)

R1+ R2=R3(at equilibrium)

In Term of magnitude

R1+ R2=R3

If force R3is removed, the remaining forces are R1, R2.

F=R1+R2

Acceleration = Force/ Mass =FM

|a|=FM=FM=R1+ R2M=R3M=R3M

Hence, acceleration on mass m is R3M


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