Question

Same force acts on two bodies of different masses $2kg\mathrm{and}4kg$ initially at rest. The ratio of times required to acquire same final velocity is

• A. $2:1$
• B. $1:2$
• C. $1:1$
• D. $4:16$

Answer 1

The correct option is B

$1:2$

Step 1: Given Data:

Mass of a first body$\left(M\right)=2kg$

Mass of a second body $\left(m\right)=4kg$

Let,

Acceleration of the first body $=A$

Acceleration of the second body $=a$

The same force acts on both bodies

The final velocity attained by them is also the same

Initial velocity $u=0$

Step 2: Formula Used:

The first equation of motion-

$v=u+at$

Where $v$ is the final velocity

$u$ is the initial velocity

$a$ is the acceleration

we know that-

$F=ma$

Step 3: Calculating the acceleration:

Since it is given that-

Force acting on both the bodies are same so,

$$\begin{gathered} MA=ma \\ \frac{a}{A}=\frac{M}{m}.............\left(1\right) \end{gathered}$$

Now using the first equation of motion,

$$\begin{gathered} v=u+at \\ v=at..............\left(2\right)(u=0) \end{gathered}$$

Suppose the time required to achieve the final velocity for the first body is $T$

The time required to achieve the final velocity for the second body is $t$

As the final velocity for both the bodies is the same,

$$\begin{gathered} v=AT=at \\ \frac{a}{A}=\frac{T}{t} \end{gathered}$$

From equations (1) and (2)-

The ratio of times required to acquire the same final velocity is-

$$\begin{gathered} \frac{T}{t}=\frac{M}{m} \\ \frac{T}{t}=\frac{2}{4} \\ \frac{T}{t}=\frac{1}{2} \end{gathered}$$

Thus, the ratio of times required to acquire the same final velocity is $1:2$.

Hence option B is the correct answer.