Question

Three blocks A, B, and C are suspended as shown in fig. Mass of each of blocks A and B is m. If the system is in equilibrium, and the mass of C is M, then:

• A. $M>2m$
• B. $M=2m$
• C. $M<2m$
• D. None of these

Answer 1

Answer: (C)

$M<2m$

Given,

Mass of block A & B $=m$

Mass of block C $=M$

Let

Mass of A $=m_A$ & Mass of B $=m_B$

Tension in string is $=T$

At equilibrium, $T=m_{A}g=m_{B}g=mg$

Weight of block C is = $Mg$

Forces on block C

$2T\cos \theta =Mg$

$\cos \theta =\frac{Mg}{2T}=\frac{Mg}{2mg}=\frac{M}{2m}$

If $0<\theta <{90}^0$ then $1>\cos \theta >0$

$1>\frac{M}{2m}>0$

$2m>M$

Hence, $2m>M$