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Question: Accelerations of the vehicle and mass m<sub>2</sub>, when pulleys are light and all surfaces are fri...

Accelerations of the vehicle and mass m2, when pulleys are light and all surfaces are frictionless, are

A

Each m2g4m1+m2\frac { m _ { 2 } g } { 4 m _ { 1 } + m _ { 2 } }

B

2 m2 g4 m1+m2,m2 g4 m1+m2\frac { 2 \mathrm {~m} _ { 2 } \mathrm {~g} } { 4 \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } } , \frac { \mathrm { m } _ { 2 } \mathrm {~g} } { 4 \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } }

C

Each 2 m1 g4 m2+m1\frac { 2 \mathrm {~m} _ { 1 } \mathrm {~g} } { 4 \mathrm {~m} _ { 2 } + \mathrm { m } _ { 1 } }

D

m1g4m2+m1,2m1g4(m2+m1)\frac { m _ { 1 } g } { 4 m _ { 2 } + m _ { 1 } } , \frac { 2 m _ { 1 } g } { 4 \left( m _ { 2 } + m _ { 1 } \right) }

Answer

2 m2 g4 m1+m2,m2 g4 m1+m2\frac { 2 \mathrm {~m} _ { 2 } \mathrm {~g} } { 4 \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } } , \frac { \mathrm { m } _ { 2 } \mathrm {~g} } { 4 \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } }

Explanation

Solution

If mass m1 travels s, m2 travels by s/2.

∴ if acceleration of m1 is a, then acceleration of mass m2 is 12\frac { 1 } { 2 } a

Here T = m1 a and m2g – 2T = m2 a2\frac { \mathrm { a } } { 2 }

Solving a = 2 m2 g4 m1+m2\frac { 2 \mathrm {~m} _ { 2 } \mathrm {~g} } { 4 \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } }