Question

A body of mass 1 kg is projected vertically up with K.E. equal to 196 J. The height at which its total K.E. is converted to its P.E. is


a.) 20 m
b.) 30 m
c.) 10 m
d.) 15 m

Please give a detailed explanation!!​

Answer 1

Given :

• Mass of Body is 1 kg .
• Kinetic Energy is equal to 196 J.

To Find :

• Height at which Kinetic Energy is coverted into Potential Energy .

Solution :

$\longmapsto\tt{Mass=1\:kg}$

$\longmapsto\tt{K.E=196\:J}$

$\longmapsto\tt{g=9.8\:{m/s}^{2}}$

As Kinetic Energy = Potential Energy .

Using Formula :

$\longmapsto\tt\boxed{Potential\:Energy=mgh}$

Putting Values :

$\longmapsto\tt{196=1\times\dfrac{98}{100}\times{h}}$

$\longmapsto\tt{196\times{10}=98h}$

$\longmapsto\tt{1960=98h}$

$\longmapsto\tt{h=\cancel\dfrac{1960}{98}}$

$\longmapsto\tt\bf{h=20\:m}$

So , The Height at which K.E is converted into P.E is 20 m....

Option a) 20 m is Correct ...

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Kinetic Energy :

The energy that is possessed by a body by the virtue of its motion is called as Kinetic Energy .

• Kinetic Energy = $\dfrac{1}{2}{mv}^{2}$

Potential Energy :

the energy that is possessed by a body by the virtue of its position (height) is called as Potential Energy .

• Potential Energy = mgh

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