Ncert Exercises & Solutions

Q. 16 A girl riding a bicycle along a straight road with a speed of 5 m/s throws a stone of mass 0.5 kg which has a speed of 15 m/s with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown? What is the change in speed, if so?

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}

= (50 + 0.5) kg = 50.5 kg.
Velocity of bicycle,

v_{1}

= 5 m/s, Mass of stone

m_{2}

= 0.5 kg
Velocity of stone

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}

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