Question

A constant force is applied on a $10kg$ mass at rest. The ratio of works done in $1st,2nd$ and $3rd$ seconds is

• A. $1:2:3$
• B. $1:3:5$
• C. $1:4:9$
• D. $1:1:1$

Answer 1

The correct option is B $1:3:5$

$\text{Step 1: Calculation of acceleration}$

Applying Newton's Law on $10kg$ mass

$\sum F=ma$ and $\sum F=F$

$\Rightarrow a=\frac{F}{m}$

As force is constant, hence acceleration will be constant during the whole motion.

$\text{Step 2: Distance travelled in}{1}^{st},2^{nd}\text{and}{3}^{rd}\text{second}.$

For constant acceleration, Distance travelled in $n^{th}$ second is given by:

$S_n=u+\frac{a}{2}[2n-1]$, Here $u=0\Rightarrow S_n=\frac{a}{2}[2n-1]$

In $1^{st}$ second, $n=1\Rightarrow S_1=\frac{a}{2}\left[2\right(1)-1]=\frac{a}{2}$

In $2^{nd}$ second, $n=2\Rightarrow S_2=\frac{a}{2}\left[2\right(2)-1]=\frac{3a}{2}$

In $3^{rd}$ second, $n=3\Rightarrow S_3=\frac{a}{2}\left[2\right(3)-1]=\frac{5a}{2}$

$\Rightarrow S_1:S_2:S_3=1:3:5$

Hence Option $\left(B\right)$ is correct.