To solve this problem, we will analyze the motion of the balls thrown by the juggler.
Let's denote:
According to the problem, the juggler throws the next ball when the first ball reaches its highest position, which implies that \(n\) balls are thrown per second.
For a ball thrown upwards, at the highest point, the velocity becomes zero. The time to reach this point is given by the first equation of motion:
\(v = u - gt\)
At the highest point, \(v = 0\), so:
\(0 = u - gt\)
\(u = gt\)
The ball should reach the maximum height by the time another ball is thrown, so:
\(t = \frac{1}{n}\), as \(n\) balls are thrown per second.
Substitute \(t = \frac{1}{n}\) into \(u = gt\):
\(u = g\left(\frac{1}{n}\right) = \frac{g}{n}\)
Now calculate the maximum height \(H\) using the formula:
\(H = \frac{u^2}{2g}\)
Substitute \(u = \frac{g}{n}\) into the equation:
\(H = \frac{\left(\frac{g}{n}\right)^2}{2g}\)
Simplify:
\(H = \frac{g^2}{2gn^2}\)
\(H = \frac{g}{2n^2}\)
Therefore, the maximum height the balls can reach is \(\frac{g}{2n^2}\).
Hence, the correct option is \(\frac{g}{2n^2}\).
\(t=\frac{u}{g}=\frac{1}{n}\)
Then,
u=\(\frac{g}{n}\)
Hmax=\(\frac{u^2}{2g}=\frac{g}{2n^2}\)
So, the correct option is (D): g/2n2
In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$) 
Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).

The rate at which an object covers a certain distance is commonly known as speed.
The rate at which an object changes position in a certain direction is called velocity.

Read More: Difference Between Speed and Velocity