Sarthaks Test
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An object is dropped from rest at a height of 150 m and simultaneously another object is dropped from rest at a height 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? 

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Initial difference in height = (150 – 100) m = 50 m 

Distance travelled by first body in 2 s = h1 = 0 + 1/ 2 g (2)2 = 2 g 

Distance travelled by another body in 2 s = h2 = 0 + 1/ 2 g (2)2 = 2 g 

After 2 s, height at which the first body will be = h1 ′ = 150 – 2 g 

After 2 s, height at which the second body will be = h2′ = 100 – 2 g 

Thus, after 2 s, difference in height = 150 – 2 g – (100 – 2 g) 

                                                        = 50 m = initial difference in height 

Thus, difference in height does not vary with time.

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