Laws Of Motion Question 318
Question: A body of mass 5 kg under the action of constant force $ \vec{F}=F _{x}\hat{i}+F _{y}\hat{j} $ has velocity at $ t=0s $ as $ \vec{v}=(6\hat{i}-2\hat{j})m/s $ and at $ t=10s $ gas$ \vec{v}=6\hat{j}\text{ m/s} $ . The force F is:
Options:
A) $ ( -3\hat{i}+4\hat{j} )\text{ N} $
B) $ ( -\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j} )\text{ N} $
C) $ ( 3\hat{i}-4\hat{j} )\text{ N} $
D) $ ( \frac{3}{5}\hat{i}-\frac{4}{5}\hat{j} )\text{ N} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] From question, Mass of body, m = 5 kg Velocity at $ t=0,u=( 6\hat{i}-2\hat{j} )m/s $ Velocity at $ t=10s,v=+6\hat{j}m/s $
Force, F=? $ a=\frac{v-u}{t}=\frac{6\hat{j}-( 6\hat{i}-2\hat{j} )}{10}=\frac{-3\hat{i}+4\hat{j}}{5}\text{ m/}{{s}^{2}} $
Force, $ F=ma=5\times \frac{( -3\hat{i}+4\hat{j} )}{5}=( -3\hat{i}+4\hat{j} )\text{ N} $
