The force exerted is:
\[ F = \frac{\Delta P}{\Delta t}. \]
Here:
\[ \Delta P = m \cdot v - 0 = 150 \times 10^{-3} \cdot 20 \, \text{kg m/s}, \]
\[ F = \frac{150 \times 10^{-3} \cdot 20}{0.1}. \]
\[ F = 30 \, \text{N}. \]
Final Answer: 30 N.
A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity):
Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is: