Question

A hemisphere S and a particle P are of same mass 'm'.P is dropped from a height 'h'.

Answer 1

An object of mass of 20 kg is dropped from a height of 4 m. Fill in the blanks in the following table by computing the potential energy and kinetic energy in each case.
height at which object is located: 4 m, 3 m, 2m, 1m, just above the ground
Potential energy
Kinetic energy
(for simplifying the calculations, take the value of g as 10 m s-2)
OR
Lets call height at 4m=A

3m=B

2m=C

1m=D

Potenial energy a A = mgh=(20 x 10 x 4 )J=800 J

Kinetic energy at A =(1/2)mv2

as we know body is stationary at A so v=0 so K.E.=0

Potential energy at B =mgh=(20 x 10 x 3)J =600J

For Kinetic energy at B

By equation off motion- v2- u2=2as

=>v2-0=2(10)(1)

=>v2=20

Kinetic energy at B=(1/2)mv2

=(1/2)(20)(20) J .......[v2=20 as proven above]

=200J

Potential energy at C =mgh=(20 x 10 x 2)J

=400J

For Kinetic energy at C

by using equation of motion-v2-u2=2as

=>v2-0=2 x 10 x 2

=>v2=40

Kinetic energy at C =(1/2)mv2

=(1/2)(20)(40) J .....[v2 = 40 as proven above]

=400J

Potential energy at D =mgh=(20 x 10 x 1)J

=200J

For Kinetic energy at D

By using equation of motion- v2 - u2=2as

=>v2 - 0=2 x 10 x 3

=>v2=60

Kinetic energy at D =(1/2)mv2

=(1/2)(20)(60) J

=600 J

hope it helps ......:)