Question

A very small groove is made in the earth and a particle of mass m is placed at a
distance r/2 from the centre. Find the escape speed of the particle from that place.​

Answer 1

Answer:

Explanation:

COMA

Answer 2

The escape speed of the particle from that place is $\sqrt{\dfrac{11GM_{e}}{4R}}$

Explanation:

Given that,

Mass = m

Distance $d=\dfrac{r}{2}$

Suppose we projected the particle with speed $v_{e}$ so that it just reaches at infinity

We need to calculate the escape speed of the particle from that place

Using conservation of energy

$K_{i}+U_{i}=K_{f}+U_{f}$

Put the value into the formula

$\dfrac{1}{2}mv_{e}^2+m[-\dfrac{GM_{e}}{2R^3}{3R^2-(\dfrac{R}{2})^2}]=0$

$\dfrac{1}{2}mv_{e}^2-\dfrac{11GM_{e}m}{8R}=0$

$v_{e}^2=\dfrac{11GM_{e}}{4R}$

$v_{e}=\sqrt{\dfrac{11GM_{e}}{4R}}$

Hence, The escape speed of the particle from that place is $\sqrt{\dfrac{11GM_{e}}{4R}}$

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Topic : escape speed

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