question_answer

A massless platform is kept on a light elastic springy as shown in Fig. 4(HT).5. When a stone of 0.1 kg mass is dropped on the pan from a height of 0.24 m, the spring compresses by 0.01 m. From what height should the stone be dropped to cause a compression of 0.04 m?

Answer:

                Here,    m = 0.1 kg, h = 0.24 m x = 0.01 m When stone is dropped from a height h and the spring is compressed by x, then loss in P.E. of particle = m g (h + x), while gain in elastic potential energy of spring will be \[\frac{1}{2}k{{x}^{2}}\] \[\therefore \]   \[mg\,\left( h+x \right)=\frac{1}{2}\,k{{x}^{2}}\] Similarly, \[mg\,\left( h'+x' \right)=\frac{1}{2}kx{{'}^{2}}\] Dividing, we get \[\frac{h+x}{h'+x'}={{\left( \frac{x}{x'} \right)}^{2}}\] \[\frac{0.24+0.01}{h'+x'}={{\left( \frac{x}{x'} \right)}^{2}}\] on solving, we get h'= 3.96m