Question

If a cricket ball hits you, it will hurt much more than a tennis ball would ,because :
A. Cricket ball is bigger
B. Cricket ball has more mass
C. Cricket ball has less density
D. None of the above

Answer 1

Here we need to apply Newton’s second law of motion. The second law gives the amount of force for a given action. We will see what factors the exerted force depends on. From that we will arrive at our solution. So let’s see what factors the magnitude of force depends on.
Formula used: $F=ma$ .

Complete answer: From Newton’s second law of motion we know that if a body has mass $m$ and acceleration$a$ ,then force exerted by this body to another body during a collision is given by
$F=ma$ , So the exerted force depends on the mass and acceleration of the body. Now let’s have a cricket ball and a tennis ball of masses $M$ and $m$ respectively.Where the cricket ball has a greater mass than the tennis ball i.e. $M > m$ So if both the balls have the same acceleration $a$ then the force exerted by the cricket ball and the tennis balls are given by
${{F}_{1}}=Ma...........(1)$ and ${{F}_{2}}=ma......(2)$ respectively. Now dividing $(1)$ by (2) we get
$\dfrac{{{F}_{1}}}{{{F}_{2}}}=\dfrac{Ma}{ma}=\dfrac{M}{m} > 1$ , because $M > m$ . So ${{F}_{1}} > {{F}_{2}}$ .

Thus the force exerted by the cricket ball is greater because it has more mass and the correct option is B.

Note:
Force exerted by a body on another body depends on mass and acceleration of the body. If the bodies have the same mass then in that case the force exerted will be greater by the body having greater acceleration. If the rate of change of momentum of both the bodies are the same then both will exert the same amount of force.