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On planet TIFR, the acceleration of an object due to gravity is half that on planet earth. An object on planet earth dropped from a height $h$ takes time $t$ to reach the ground. On planet TIFR, how much time would an object dropped from height $h$ take to reach the ground?

  1. $\left(\dfrac{t}{\sqrt{2}}\right)$
  2.  $\sqrt {2}t$
  3.   $2t$
  4. $\left(\dfrac{h}{t}\right)$
  5. $\left(\dfrac{h}{2t}\right)$
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2 Answers

Best answer
8 votes
8 votes

Let, The acceleration due to gravity on earth =$g.$

and the acceleration due to gravity on $TIFR = G=\dfrac{g}{2}.$

Time taken to reach the ground on earth $= t = \sqrt{\dfrac{2h}{g}}$.

Similarly, on TIFR planet, time taken = T = $\sqrt{\dfrac{2h}{G}}$.= $\sqrt{\dfrac{4h}{g}}$.

$\Rightarrow T = \sqrt{2}t.$

Ans - Option (b)

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3 votes

Using basic laws of kinematics :

h = 1/2 a t2   for an object relaesed from top which is initially at rest

So a = g for earth we can write :

t1  =  sqrt (2h / g)

Now according to the question

acceleration due to gravity in TIFR planet =  g / 2

So t2  = sqrt(4h / g)  = sqrt(2) *  sqrt (2h / g)

                              = sqrt(2) * t1 ..

Hence B) should be corrected answer..Only sqrt(2) should be there and 't' should be separate..Hence sqrt(2) * t is correct option..

Answer:

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