Question

A golf ball of mass $0.05\;kg$ placed on a tee, is struck by a gold stick. The speed of the golf ball as it leaves the tee is $100m/s$, the time of contact between them is $0.02\;s$. If the force decreases to zero linearly with time, then the force at the beginning of contact is:
\[\begin{align}
  & A.500N \\
 & B.250N \\
 & C.200N \\
 & D.100N \\
\end{align}\]

Answer 1

Hint: We know from Newton’s second law that force is proportional to the acceleration of the given body. We also know from the definition of acceleration, that acceleration is the rate of change of velocity with respect to time. Using these two we can solve the given sum.

Formula used:
$F=ma$ and $a=\dfrac{v}{t}$

Complete step-by-step answer:
Here, given that the mass of the golf ball is $m=0.05\;kg$ and the speed of the golf ball is $u=100m/s$. The time of interaction between the golf and the tee is $t=0.02s$. Since the velocity of the force decreases after the collision, we can say that $v=0$. Then from the definition of the average acceleration $a=\dfrac{v-u}{\delta t}$
$\implies a=\dfrac{100-0}{0.02}=5\times 10^{3}m/s^{2}$
From the newton’s second law of motion, we know that , the force acting on any given object is proportional to the acceleration of the object, then the $F$ on the golf is given as
$F=ma$
$\implies F=0.05\times 5\times 10^{3}=250N$
Thus the correct option is $B.250\;N$

So, the correct answer is “Option B”.

Additional Information: We know that Newton's laws of motion describes the relationship between the force acting on a body and its motion. These are also the foundations of classical mechanics, also known as Newtonian mechanics. The three laws are given as:
1. An object remains in its state of motion or rest until an external force acts on it.
2. The force applied on an object is equal to the product of its mass and acceleration.
3. Every action has an equal and opposite reaction.

Note: We know that Force is a vector quantity, which has both magnitude and direction. Here, the direction of the force is the same as the direction of acceleration of the golf ball. We can also find the acceleration of the golf, from the equation of motion, $v=u+at$