Question

A 2kg block is dropped from a height of 0.4 m on a spring of force constant $K = 1960 \mathrm { Nm } ^ { - 1 }$. The maximum compression of the spring is

• A. 0.1 m
• B. 0.2 m
• C. 0.3 m
• D. 0.4 m

Answer 1

Answer: (A)

0.1 m

Answer 2

When a block is dropped from a height, its potential energy gets converted into kinetic energy and finally spring get compressed due to this energy.

∴ Gravitational potential energy of block = Elastic potential energy of spring

⇒ $m g h = \frac { 1 } { 2 } K x ^ { 2 }$

⇒ $x = \sqrt { \frac { 2 m g h } { K } } = \sqrt { \frac { 2 \times 2 \times 10 \times 0.4 } { 1960 } }$ $= 0.09 \mathrm {~m} \simeq 0.1 \mathrm {~m}$.