Question

A block of mass 2 kg is dropped from a height of 40 cm on a spring whose force-constant is $1960 \mathrm {~N} \mathrm {~m} ^ { - 1 }$ . The maximum distance through which the spring is compressed by:

• A. 5 cm
• B. 15 cm
• C. 20 cm
• D. 10 cm

Answer 1

Answer: (D)

10 cm

Answer 2

$\operatorname { mg } ( \mathrm { h } + \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { kx } ^ { 2 }$

Here, m = 2kg, h = 40 cm

$\mathrm { k } = 1960 \mathrm { NmH } ^ { - 1 }$ and $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$

$\therefore 2 \times 10 ( 0.40 + \mathrm { x } ) = \frac { 1 } { 2 } \times 1960 \mathrm { x } ^ { 2 }$

On solving, we get x = 10 cm.