Question

A 15 g ball is shot from a spring gun whose spring has a force constant $600 \mathrm { Nm } ^ { - 1 }$ . The spring is compressed by 5 cm. The greatest possible horizontal, range of the ball for this compression (Take $\mathrm { g } = 10 \mathrm {~ms} ^ { - 2 }$ )

• A. 6 m
• B. 8 m
• C. 10 m
• D. 12 m

Answer 1

Answer: (C)

10 m

Answer 2

Here, $\mathrm { R } _ { \max } = \frac { \mathrm { u } ^ { 2 } } { \mathrm {~g} } = \frac { 1 } { 2 } \mathrm { mu } ^ { 2 } \times \frac { 2 } { \mathrm { mg } }$

But $\frac { 1 } { 2 } \mathrm { mu } ^ { 2 } = \frac { 1 } { 2 } \mathrm { kx } ^ { 2 }$

$\therefore \mathrm { R } _ { \max } = \frac { 1 } { 2 } \mathrm { kx } ^ { 2 } \times \frac { 2 } { \mathrm { mg } } = \frac { \mathrm { kx } ^ { 2 } } { \mathrm { mg } } = \frac { 600 \times ( 0.05 ) ^ { 2 } } { 0.015 \times 10 } = 10 \mathrm {~m}$