Question

A compressed spring of spring constant k releases a ball of mass m. If the height of spring is h and the spring is compressed though a distance x, the horizontal distance covered by ball to reach ground is

• A. x$\sqrt { \frac { \mathrm { kh } } { \mathrm { mg } } }$
• B.
• C. x$\sqrt { \frac { 2 \mathrm { kh } } { \mathrm { mg } } }$
• D. $\frac { \mathrm { mg } } { \mathrm { x } \sqrt { \mathrm { kh } } }$

Answer 1

Answer: (C)

x$\sqrt { \frac { 2 \mathrm { kh } } { \mathrm { mg } } }$

Answer 2

Spring energy = kinetic energy

i.e., $\frac { 1 } { 2 }$kx² = $\frac { 1 } { 2 }$ mv² or v = x $\sqrt { \frac { \mathrm { k } } { \mathrm { m } } }$

Time taken by ball to reach ground, t

= $\frac { 1 } { 2 }$ at²)

∴ Horizontal distance covered = vt

= x