Question

The force constant of a spring gun is$50N/m$. If a ball of 20g be shoot by the gun, So that its spring is compressed by 10cm, the velocity of the ball is:
A. $5m/s$
B. $15m/s$
C. $25m/s$
D. $20m/s$

Answer 1

Hint This question can be solved with the concept of conservation of energy. In this question, there is potential energy in spring, which while hitting, is converted to the kinetic energy of the ball. Compare and equate the equations of potential energy and kinetic energy. Solve it, and you will get the answer.

Complete step-by-step solution :
Using the concept of conservation of energy:
Initially before hitting the ball, both the spring and ball’s kinetic energy is zero.
Potential energy stored in spring $= \dfrac{{k{x^2}}}{2} - - - (1)$
While hitting the ball, this potential energy of spring is converted to kinetic energy of the ball.
So, kinetic energy of the ball is given by =$\dfrac{{m{v^2}}}{2} - - - (2)$
Equating equation $(1)$ and$(2)$:
$\dfrac{{k{x^2}}}{2} = \dfrac{{m{v^2}}}{2} \\\ \dfrac{{k{x^2}}}{2} = {v^2} \\\ v = \sqrt {\dfrac{{k{x^2}}}{m}} \\\$
Now, as per the question:
$k =$Spring constant
$x =$Distance travelled by spring
$m =$Mass of ball
Putting values from question:
$v = \sqrt {\dfrac{{50 \times {{(10 \times {{10}^{ - 2}})}^2}}}{{20}}}$
Solving, we get:
$v = 5m/s$

Note:- Always take care of unit conversion. Here all the answers are given in terms of $m/s$.so all the units should be in $m$ or $s$. For example, in this question compression of string is given in $cm$, so we have to convert it in $m$.