Question

The displacement of centre of mass of $A_B$ system till the string becomes vertical is:

• A. zero
• B. $L(1-cos\theta )$
• C. $\frac{L}{2}(1-cos\theta )$
• D. None of these

Answer 1

The correct option is C $\frac{L}{2}(1-cos\theta )$

$\frac{L}{2}(1-\cos \theta )$

$\Rightarrow △y$Center of mass $=\frac{m_1{△y}_1+m_2{△y}_2}{m_1+m_2}$

$\Rightarrow {△y}_1=0$

${△y}_2=mL(1-\cos \theta )$

${△y}_{Lm}=\frac{m\times 0+mL(1-\cos \theta )}{2m}$

$=\frac{L-L\cos \theta }{2}$

$=\frac{L}{2}(1-\cos \theta )$

Hence, the answer is $\frac{L}{2}(1-\cos \theta ).$