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Block A of mass m/2 is connected to one end of light rope which passes over a pulley as shown.Man of mass m climbs the other end of rope with a relative acceleration of g/6 wrt rope ,find acceleration of block A and tension in rope.

Block A of mass m/2 is connected to one end of light rope which passes over a pulley as shown.Man of mass m climbs the other end of rope with a relative acceleration of g/6 wrt rope ,find acceleration of block A and tension in rope.

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Grade:11

1 Answers

Arun
25750 Points
5 years ago

The accelaration of man with respect to ground is

g=a+a0

hence

a=g-a0

From force diagram of man

T-mg=ma

T-mg=m(g-a0)

T-mg=mg-ma0

T+ma0=2mg................1

From force diagram of block A

T-m/2*g=m/2*a0.

T+m/2*a0=m/2*g...............2

subtracting equation 2 and 1

T+m/2*a0-(T+ma0)=m/2g-2mg

m/2a0-ma0=-3mg/2

-ma0/2=-3mg/2

ma0/2=3mg/2

a0=3g

From Equation 2

T+m/2*a0=m/2*g

T=m/2g-m/2a0

T=m/2g-m/2*3g

T=-2gm

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