Three masses M = 100 kg , m 1 = 10 kg and m 2 = 20 kg are arranged in a system as shown in figure. All the surfaces 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 m 2 moves upward…

Question

Three masses M = 100 kg , m 1 = 10 kg and m 2 = 20 kg are arranged in a system as shown in figure. All the surfaces 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 m 2 moves upward with an acceleration of 2 ms - 2 . The value of F is (Take g = 10 ms - 2 )

Aicharya · Accepted Answer

Let acceleration of $100 \mathrm{~kg}$ block $=a_1$
FBD of $100 \mathrm{~kg}$ block w.r.t ground

$\mathrm{F}-\mathrm{T}-\mathrm{N}_1=100 \mathrm{a}_1$ ... (i)
FBD of 20 block wrt $100 \mathrm{~kg}$

$\mathrm{T}-20 \mathrm{~g}=20(2)$
$\mathrm{T}=240$ ... (ii)
$\mathrm{~N}_1=20 \mathrm{a}_1$ ... (iii)
FBD of $10 \mathrm{~kg}$ block wrt $100 \mathrm{~kg}$

$10 \mathrm{a}_1-240=10(2)$
$\mathrm{a}_1=26 \mathrm{~m} / \mathrm{s}^2$
$\mathrm{~F}-240-20(26)=100 \times 26$
$\Rightarrow \mathrm{F}=3360 \mathrm{~N}$

Three masses M = 100 kg , m 1 = 10 kg and m 2 = 20 kg are arranged in a system as shown in figure. All the…

Solution