Question

Block A of weight $500N$ and block B of weight $700N$ are connected by rope pulley system as shown in the figure. The largest weight C in N that can be suspended without moving block A and B in Newton is (The coefficient of friction for all plane surfaces of contact is $0.3$. The pulleys are ideal.):

• A. $810$
• B. $90$
• C. $270$
• D. $900$

Answer 1

Answer: (A)

$810$

From FBD of block A, $T=f=\mu \left(m_{A}g\right)=500\mu =500\times 0.3=150N$ ...(1),

where given weight of A is $m_{A}g=500N$
Now for block B:

$f+(T+2T)+f^{\prime }=T^{\prime }+f$

$3T+\mu (m_{A}g+m_{B}g)=T^{\prime }$

$3T+0.3\times (500+700)=T^{\prime }$
$3T+360=T^{\prime }$ ...(2)

For block C:

$T^{\prime }=W$ ....(3) where $W=$ weight of block C such that blocks A and B will not move.
Using (1), (2) and (3), $W=450+360=810N$