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In fig. both pulleys and the string are ...

In fig. both pulleys and the string are massless and all the surfaces are frictionless.

Given `m_(1)=1kg, m_(2)= 2kg, m_(3)=3kg`.
The acceleration of `m_(3)` is

A

`(40)/(7) ms^(-2)`

B

`(30)/(7) ms^(-2)`

C

`(20)/(7) ms^(-2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Free-body diagrams

Constraint relation :
`x_(1)=x_(2)+x_(3)`
`a_(1)=a_(2)+a_(3)`
Equation of motion :
`T-N=m_(1)a_(1)` …(i)
`N=m_(2)a_(1)`..(ii)
`m_(2)g-T=m_(2)a_(2)` …(iii)
`m_(3)g-T=m_(3)a_(3)` ..(iv)
Using above equations, we can calculate the values.
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Knowledge Check

  • In fig. both pulleys and the string are massless and all the surfaces are frictionless. Given m_(1)=1kg, m_(2)= 2kg, m_(3)=3kg . The acceleration of m_(1) is

    A
    `(40)/(7) ms^(-2)`
    B
    `(30)/(7) ms^(-2)`
    C
    `(20)/(7) ms^(-2)`
    D
    `(sqrt(17)g)/(7) ms^(-2)`

  • In fig. both pulleys and the string are massless and all the surfaces are frictionless. Given m_(1)=1kg, m_(2)= 2kg, m_(3)=3kg . Find the tension in the string

    A
    `(120)/(7)N`
    B
    `(240)/(7)N`
    C
    `(130)/(7)N`
    D
    None of these

  • If m_(1) = 10kg, m_(2)= 4kg, m_(3)= 2kg , the acceleration of system is

    A
    `5g//2`
    B
    `5g//3`
    C
    `5g//8`
    D
    `5g//14`

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