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Question

An object is dropped from rest at a height of 150 m and simultaneously another object is dropped from rest at a height of 100 m. What is the difference in their heights after 2 s if both the objects drop with same accelerations? How does the difference in heights vary with time?

A
30 m
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B
40 m
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C
50 m
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D
60 m
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Solution

Step 1: Given that:

The objects are dropped from rest that is

The initial velocity of both objects = u1=u2=0

Height from which the fist object is dropped= H1=150m

Height from which the second object is dropped at the same time= H2=100m

Acceleration ion first body= Acceleration in the other body

Given time(t) = 2sec
Step 2: Calculation of the distance covered by both the bodies in 2sec:

The distance covered by a body in downward direction under acceleration due to gravity that is g is given by;

h=ut+12gt2

For u=0

h=0+12gt2

h=12gt2

Now,

The distance travelled by the first body in 2s will be;

h1=12g×(2s)2

h1=12g×4

h1=2g

The distance travelled by the other body in the same 2s will be given by;

h2=12g×(2s)2

h2=12g×4

h2=2g

Step 3: Calculation of the difference in their heights after 2s:

The difference in the heights of both the bodies initially is given by;

=H1H2

=150m100m

=50m

After 2s,

The height at which the first body will be given by;

=H1h1

=150m2g

=1502g

The height at which the other body will be given by;

=H2h1

=100m2g

=1002g

Now,

The difference in their heights will be given by:

=(H1h1)(H2h2)

=(1502g)(1002g)

=1502g100+2g

=50m

Which is the same as the difference in their heights initially.
Thus,

It is clear that the difference in their heights is 50m and it does not vary with time.

Thus,

Option C) 50m is the correct option.


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