Correct Answer - Option 4 :
\(\frac{1}{\sqrt m}\)
CONCEPT:
Newton's second law of motion
- According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the applied unbalanced force.
- The magnitude of the force is given as,
\(\Rightarrow F=ma\)
CALCULATION:
Given m = mass, initial velocity u = 0 m/s and F = constant
- Since force is constant so the produce acceleration in the body will also be constant.
- By Newton's second law of motion, the produce acceleration in the body is given as,
\(\Rightarrow a=\frac{F}{m}\) -----(1)
By the third equation of motion,
\(\Rightarrow v^{2}=u^{2}+2as\) -----(2)
Where v = final velocity, u = initial velocity, a = constant acceleration and s = displacement
By equation 2,
\(\Rightarrow v^{2}=0^{2}+2as\)
\(\Rightarrow v^{2}=\frac{2Fs}{m}\)
\(\Rightarrow v=\sqrt{\frac{2Fs}{m}}\) -----(3)
In equation 3, F and s are constant so,
\(\Rightarrow v\propto\frac{1}{\sqrt{m}}\)
- Hence, option 4 is correct.
