Question

A ball is dropped from a height h=r above earth surface.the speed with which ball strikes the surface of earth

Answer 1

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Answer 2

Concept

Speed is measured because the ratio of distance to the time within which the space was covered. Speed could be a scalar quantity because it has only direction

Given

We are only if the ball is dropped from the peak $h=r$ above earth surfaces.

Find

We have to seek out the speed with which ball strikes the earth surface.

Solution

A body released from the peak is capable the radius of the planet.

As the height above the surface of earth.

$\text{Mechnical Energy},E_{1}=K.E.+P.E.$

$E_{1}=0-\frac{GMm}{2R}=-\frac{GMm}{2R}$                      ......(1)

As the surface of earth,

$E_{2}=\frac{1}{2}mv^2-\frac{GMm}{R}$                                 ......(2)

From the laws of conservation of energy,

$\begin{aligned}E_{1}&=E_{2}\\ -\frac{GMm}{2R}&=\frac{1}{2}mv^2-\frac{GMm}{R}\\ \frac{1}{2}mv^2&=\frac{GMm}{2R}\\ v&=\sqrt{\frac{GMR}{R^2}}\end{aligned}$          ......(3)

As we know, $g=\frac{GM}{R^2}$

From equation (3), we get

$v=\sqrt{gR}$

Hence, the speed with which ball strikes the surface of earth is $\sqrt{gR}$.

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