Question

A large stone of mass Me/2 is released when centre of mass of the stone is at a height h(h<<Re). Find speed of stone when it is at a height of h/2. Me and Re are mass and radius of earth. Given h=3/20m

Answer 1

Answer:

this answer is wrong. the correct answer is 1

Answer 2

Final Answer:

The speed of stone of mass Me/2 at the height of h/2, which is released when the centre of mass of the stone is at a height h(h<<Re) is $\sqrt{2gh}$ and the value is 1.72 metre/second for h=3/20m.

Given:

The large stone of mass Me/2 is said to be released when the centre of mass of the stone is at a height h(h<<Re).

Me and Re are the mass and the radius of earth.

Also it is given h=3/20m.

To Find:

The speed of stone of mass Me/2 at the height of h/2, which is released when the centre of mass of the stone is at a height h(h<<Re) is to be calculated.

Explanation:

The vital concepts important for figuring out the solution here are.

• The kinetic energy of a body is half of the product of the mass and the velocity of the referred body squared.
• The potential energy of a body is the product of the mass, its height and the acceleration due to gravity.

• The concept of conservation of energy indicates here that the final sum of the potential energy and the kinetic energy is equal to the initial sum of the potential energy and the kinetic energy .

Step 1 of 3

As per the given statement in the problem, the following is the valid equation applying the concept of conservation of energy.

$KE_2=PE_2-PE_1\\\frac{1}{2} \frac{M_E}{2}v^2=\frac{M_Egh}{2} -\frac{M_Egh}{4} \\\frac{1}{2} \frac{M_E}{2}v^2=\frac{M_Egh}{2}$

Step 2 of 3

Using the information in the given problem, solve the equation in the following way.

$\frac{1}{2} \frac{M_E}{2}v^2=\frac{M_Egh}{2} \\v^2=2gh\\v=\sqrt{2gh}$

Step 3 of 3

In continuation with the above calculations, the speed of the stone is

$v\\=\sqrt{2gh}\\=\sqrt{\frac{2\times 3g}{20}}\\=\sqrt{\frac{3\times 9.8}{10}}\\=1.7\;m/s$

Therefore, the required correct answer is the speed $\sqrt{2gh}$ which is 1.7 metre/second for h=3/20m.

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