Question

A massless string and a spring connect two blocks $A$ and $B$ to each other. Block $B$ slides over a frictionless inclined plane while block A slides over horizontal surface. Coefficient of friction between block A horizontal surface is $\mu=0.2 .$ At the instant shown blocks are moving with constant speed. Mass of block $A$ and energy stored in spring are respectively. $\left[g=10 m / s ^{2}, m _{ B }=2 kg \right]$

• A. $5 \, kg, \, 1J$
• B. $10 \, kg, \, 0.05 \, J$
• C. $5 \, kg, \, 0.05 \, J$
• D. $10 \, kg, \, 1J$

Answer 1

Answer: (C)

$2 g \sin \theta=k x=\mu m_{A} g$
$\Rightarrow m _{ A }=\frac{2 g \sin \theta}{\mu g }=\frac{2 \sin \theta}{\mu}=\frac{2 \times \frac{1}{2}}{0.2}=5 kg$
$kx =2 \times 10 \times \frac{1}{2}=10$
$x =\frac{10}{1 \times 10^{3}}=1 cm$
$\Rightarrow $ Energy $=\frac{1}{2} \times 10^{3} \times\left(10^{-2}\right)^{2}=0.05$ Joule