Question

In the arrangement shown in figure pulleys are small, light and frictionless. Threads are inextensible and masses of blocks A, B and C are $m_1=5$ kg, $m_2=4$ kg and $m_3=2.5$ kg respectively. Coefficient of friction for both the planes is $=0.50$.
Acceleration of block B (in $m/s^2$) is :

• A. 3
• B. 2
• C. 4
• D. none of these

Answer 1

Answer: (D)

none of these

Let the acceleration of A , B and C be $a_1$ ,$a_2$ and $a_3$

For block A

$T+m_{1}gsin37-m_{1}gcos37\times \mu =m_1{a}_1$

$T+10=5a_1$ ...(1)

The maximum tension rope can be $T_{max}=m_{3}g/2=\frac{2.5g}{2}=12.5N$

Maximum friction for block B $f_{max}=\mu m_{2}g=0.5\times 4g=20N$

So block B will remain in rest ,$f_{max}>T_{max}$

$a_2=0$ ...(2)

for block C

$m_{3}g-2T=m_3{a}_3$

$25-2T=2.5a_3$ ..(3)

by constraint relation

$a_1+a_2=2a_3$ ..(4)

on solving above 4 equation

we get $a_1=4m/s^2$

$a_2=0m/s^2$

$a_3=2m/s^2$