A force of 10 N acts on 5 kg for 2 seconds. The same force acts on 2.5 kg for 2 seconds. Compare the momentum produced and compare the acceleration caused? [3 MARKS]

Open in App

Solution

Solution:2.5 Marks
Reasoning: 0.5 Marks
Given, force on first body, $F_{1} = 10 N$ . force on second body, $F_{2} = 10 N$ , mass of first body, $m_{1} = 5 k g$ , initial velocity of first body, $u_{1} = 0$ , initial velocity of second body, $u_{2} = 0$ , mass of second body, $m_{2} = 2.5 k g$ and time, $t = 2 s$ .
$S t e p 1$ :
Let acceleration produced on first body be $a_{1}$ .
Force on first body be $F_{1}$ and final velocity of first body be $v_{1}$ .
According to Newton's second law,
$F o r c e = m a s s \times a c c e l e r a t i o n$
So, $F_{1} = m_{1} a_{1}$
$10 = 5 \times a_{1}$
$\Rightarrow$ $a_{1} = \frac{10}{5} = 2 m s^{- 2}$
From $1^{s t}$ equation of motion,
$a_{1} = \frac{v_{1} - u_{1}}{t} = \frac{v_{1} - 0}{2}$
$\Rightarrow$ $v_{1} = 4 m s^{- 1}$
$S t e p 2$ :
Let acceleration produced on second body be $a_{2}$ , force on second body be $F_{2}$ and final velocity of second body be $v_{2}$ .
According to Newton's second law,
$F o r c e = m a s s \times a c c e l e r a t i o n$
So, $F_{2} = m_{2} a_{2}$
$10 = 2.5 \times a_{2}$
$\Rightarrow$ $a_{2} = \frac{10}{2.5} = 4 m s^{- 2}$
From $1^{s t}$ equation of motion
$a_{2} = \frac{v_{2} - u_{2}}{t} = \frac{v_{2} - 0}{4}$
$\Rightarrow$ $v_{2} = 8 m s^{- 1}$
Let momentum of first body be $P_{1} = m_{1} v_{1}$ and second body be $P_{2} = m_{2} v_{2}$ .
Comparing momentum= $\frac{P_{1}}{P_{2}} = \frac{m_{1} v_{1}}{m_{2} v_{2}} = \frac{5 \times 4}{2.5 \times 8} = \frac{20}{20} = 1 : 1$ .
Comparing acceleration $= \frac{a_{1}}{a_{2}} = \frac{2}{4} = 1 : 2$ .

Conclusion: In this equation, Since the force applied on two bodies is same we observe that the ratio of change in momentum remains same even though the ratio of acceleration is different.

Suggest Corrections

Similar questions

A force of 10 N acts on 5 kg for 2 seconds. The same force acts on 2.5 kg for 2 seconds. Compare the momentum produced and compare the acceleration caused? [3 MARKS]

A force of 50 N acts on a stationary body of mass 10 kg for 2 seconds. Find the acceleration produced in the body and velocity attained by it.

Q. Force shown acts for

2

seconds. Find out work done by force

F

10

kg in

3

seconds.

A force of 10 Newton acts on a body of mass 2kg for 3seconds initially at rest calculate velocity acquired by the body and change in momentum of the body

A force of 10 N acts on a body of mass 5 kg. Find the acceleration produced.

Join BYJU'S Learning Program