Three masses M = 100kg, m₁ = 10kg and M₂ = 20kg are arranged in a system as shown in figure. All the surface are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m₂ moves upward with an acceleration of 2ms^-2. The value of F is:

(Take g = 10ms^-2)

Option 1 -  3360 N

Option 2 - 3380

Option 3 - 3120 N

Option 4 - 3240 N

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Answered by

Vishal Baghel | Contributor-Level 10

7 months ago

Correct Option - 1

Detailed Solution:

Given Acceleration of m₂ is 2m/s²

(upward)

N = 20a T – m₂g = m₂a

T – 20g = 20a

T = 200 + 20 * 2

T = 240 N

T = m₁ a₁

240 = 10a₁

a₁ = 24 m/s²

$\Rightarrow T a + T a_{1} - T a_{2} = 0$

$a_{2} = 24 + 2 = 26 m / s^{2}$

F – T – N = Ma₂

F – 240 = 100 * 26 + 20 * 26

F = 3360 N

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