Question

A massless platform is kept on a light elastic spring as shown in fig. When sand particles of 0.1 kg mass are dropped on the pan from a height of 0.24 m. The particle strikes the pan and the spring is compressed by 0.001 m. From what height should the particle be dropped to cause a compression of 0.04 m-

• A. 0.96 m
• B. 2.96 m
• C. 3.96 m
• D. 0.48 m

Answer 1

Answer: (C)

3.96 m

From conservation of energy,
$mg(h+x)=\frac{1}{2}k{x}^2$
Case I $mg(0.24+0.01)=\frac{1}{2}k(0.01{)}^2$
Case II $mg(h+0.04)=\frac{1}{2}k(0.04{)}^2$
dividing $\frac{h+0.04}{0.24+0.01}=\frac{16}{1}$
$\therefore h+0.4=16\times 0.25=4$
$h=3.96$ m.