A stone is dropped from a height h. It hits the ground with a certain momentum p. If the stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by A) 68% B) 41% C) 200% D) 100% - Padhle.Online
Students' favourite free learning app with LIVE online classes, instant doubt resolution, unlimited practice for classes 6-12, personalized study app for Maths, Science, Social Studies, video e-learning, online tutorial, and more. Download Now!

A stone is dropped from a height h. It hits the ground with a certain momentum p. If the stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by A) 68% B) 41% C) 200% D) 100%

 answer: (B) 41%

Explanation

A stone is dropped from a height of h in the first scenario. We may deduce from the equations of motion that the velocity of the stone in free fall is given by:

v = √2gh——(1)

where

  • g is the acceleration due to gravity
  • h is the height from which the stone is dropped.

Also, the momentum of the stone is given by

p=mv——(2)

where

  • p is the momentum of the stone
  • m is the mass of the stone
  • v is the velocity of the stone

Let this be equation 2. Substituting equation 2 in equation 1, we have

p = mv = m√2gh−−−(3)

Now, let us move on to the second case.

Here, the stone is dropped from a height 100% more than the previous height.

If we call this height H, it is given by

H = h + 100/100h = 2h

Again, if we take the velocity of this stone to be V, it is given by

V=√2gH =√2g(2h) 2√gh−−–(4)

Similarly, if the momentum of the stone in the second case is P, it is given by

P = mV = m2√gh−−–(5)

Now, to calculate the change in momentum, we subtract equation 3 from equation 5, as follows

P−p=mV−mv=m2√gh – m√gh = m√gh (√2-1) = 0.41m√gh

finally, to get the change in momentum in percentage, we take the ratio of this change in momentum to the original momentum and multiply by 100%.

This is shown as follows.

P−p/p x 100% 0.41m√gh/ m√gh x 100% =41%

Was this answer helpful?

 

About the Author

Principal, Babu Daudayal SVM, Mathura

Post a Comment

Cookie Consent
We serve cookies on this site to analyze traffic, remember your preferences, and optimize your experience.
Oops!
It seems there is something wrong with your internet connection. Please connect to the internet and start browsing again.
AdBlock Detected!
We have detected that you are using adblocking plugin in your browser.
The revenue we earn by the advertisements is used to manage this website, we request you to whitelist our website in your adblocking plugin.
Site is Blocked
Sorry! This site is not available in your country.