Ncert Exercises & Solutions

A girl riding a bicycle along a straight road with a speed of

5

$5$ m/s throws a stone of mass

0.5

$0.5$ kg which has a speed of

15

$15$ m/s with respect to the ground along her direction of motion. The mass of the girl and bicycle is

50

$50$ kg. What is the change in speed of the bicycle after the stone is thrown?

1.	$0.1~\text{m/s}$
2.	$0.7~\text{m/s}$
3.	$1~\text{m/s}$
4.	$5~\text{m/s}$

Hint: Use law of conservation of linear momentum

Step 1: Apply linear momentum conservation to calculate the speed of the bicycle after the stone is thrown.

Given, total mass of girl, bicycle and stone

m_{1}

$m_{1}$ = (50 + 0.5) kg = 50.5 kg.
Velocity of bicycle,

v_{1}

$v_{1}$ = 5 m/s, Mass of stone

m_{2}

$m_{2}$ = 0.5 kg
Velocity of stone

v_{2}

$v_{2}$ = 15 m/s, Mass of girl and bicycle m = 50 kg
Yes, the speed of the bicycle changes after the stone is thrown.
Let after throwing the stone the speed of the bicycle be v m/s.
According to law of conservation of linear momentum,

$\begin{array}{l} m_{1} u_{1} = m_{2} u_{2} + mv \\ 50 .5 \times 5 = 0 .5 \times 15 + 50 \times v \\ 252 .5 - 7 .5 = 50 v \\ or v = \frac{245 .0}{50} \\ v = 4 .9 m / s \\ Change in speed = 5 - 4 .9 = 0 .1 m / s \end{array}$

NEET Information

courses

Company

Botany Questions

Chemistry Questions

Physics Questions

Zoology Questions