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Pseudo Force

A man of mass...

Question

A man of mass $m$ slides down along a rope that is connected to the ceiling of an elevator with deceleration $a$ relative to the rope. If the elevator is going upward with an acceleration $a$ relative to the ground, then tension in the rope is

A

m g

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B

m (g + 2 a)

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C

m (g + a)

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D

zero

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Solution

The correct option is B $m (g + 2 a)$
Net acceleration of man w.r.t ground,
$= a - (- a) = 2 a$

From the given figure we get the force equation as
$T - m g = m (2 a)$
$∴ T = m (g + 2 a)$

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