Question

A block of mass 250 g is kept on a vertical spring of spring constant 100 N/m fixed from below. The spring is now compressed to have a length 10 cm shorter than its natural length and the system is released from this position. How high does the block rise from this position? Take g = 10 m/$s^2$.

• A. 300 cm
• B. 30 cm
• C. 200 cm
• D. 20 cm

Answer 1

The correct option is D

20 cm

$U_i+K{E}_i=U_f+K.E_f$

$U_i=\frac{1}{2}K{x}^2$

= $\frac{1}{2}\times 100\times (0.1{)}^2$

= $\frac{1}{2}J$

Assuming Point of maximum compression is at zero gravitational potential.

$U_f$ = mgh

$\Rightarrow U_i=U_f$

$\Rightarrow \frac{1}{2}=0.250\times 10\times h=\frac{250}{1000}\times 10\times h$

$\Rightarrow h=\frac{100}{2}<\frac{1}{250}=\frac{1}{5}$

= 0.2 m

= 20 cm