Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

JEE Class main Answered

law of conservation of energy in case of freely falling body
Asked by mdowaisraza581 | 16 May, 2023, 10:06: PM
answered-by-expert Expert Answer
Let the body is dropped from height h . Just before dropping it has only potential energy (mgh) ,
where m is mass of body, g is acceleratio due to gravity and h is height.
 
Hence intial total energy Ei  is
 
 begin mathsize 14px style E subscript i space equals space m space g space h end style  ................................... (1) 
 
Let us consider it has fallen a distance y from initial point .
 
Potential energy U at this point is 
 
begin mathsize 14px style U space equals space m space g space left parenthesis h minus y right parenthesis end style   ...............................(2)
 
Speed of body at this point is determined from the following equation
 
begin mathsize 14px style v squared space equals space 2 g y end style
Hence kineti energy K at this point is 
 
begin mathsize 14px style K space equals space 1 half m space v squared space space equals space 1 half m space left parenthesis space 2 space g space y space right parenthesis space equals space left parenthesis space m space g space y space right parenthesis space end style
Total energy Ey at this point is sum of potential energy and kinetic energy
 
begin mathsize 14px style E subscript y space equals space U space plus space K space equals space m g left parenthesis h minus y right parenthesis space plus space left parenthesis space m g y space right parenthesis space equals space m g h end style  ...........................(3)
 
Finally, when the body reaches ground , its potential energy is zero and has only kinetic energy.
 
Final kinetic energy Kf is
 
begin mathsize 14px style K subscript f space equals space 1 half m space v subscript f squared space end style
where vf is the final speed when body reaches the ground. 
 
Final speed vf is determined from the following equation
 
begin mathsize 14px style v subscript f superscript 2 space equals space 2 space g space h space end style
Hence final kinetic energy , or total energy at ground is
 
 begin mathsize 14px style E subscript f space equals space K subscript f space equals space 1 half m space v subscript f superscript 2 space equals space 1 half m space left parenthesis space 2 space g space h space right parenthesis space equals space m space g space h end style  ......................................(4)
 
Hence from eqn.(1) , eqn.(3) and eqn.(4) , we see that total energy always remain same as ( m g h ) . 
 
This is due to conservation of energy.  At a height h, all total energy is in the form of potential energy.
 
After falling a distance y from starting point , potential energy decreases but kinetic energy increases .
 
We found that sum of potential energy and kinetic energy is ( m g h ) .
 
When the body is reaching ground, just before hitting the ground , it has only kinetic energy that equals ( m g h ) .
 
Hence loss in potential energy equals gain in kinetic energy so that sum of kinetic enrgy and potential energy at all the points is same.
Answered by Thiyagarajan K | 17 May, 2023, 11:27: AM
Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
JEE main - Physics
Help me
question image
Asked by nandichandi33 | 24 Mar, 2024, 09:21: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Physics
The work done in moving a body of mass m up an inclined plane of inclination θ to the horizontal, height h and length l ( no friction ) are related as
Asked by sarthakbhoskar7630 | 05 Mar, 2024, 07:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Physics
A uniform rod of length L and mass M has been placed on a rough horizontal surface. The force F applied on the rod is such that the rod is such that the rod is just in the state of rest. If the coefficient of friction varies according to the relation μ=KX, where K is a positive constant. Suppose friction is present only from X=0 to X=L. If the rod moves in the direction of application of force then the total heat generated in the time in which the rod crosses this region, is equal to
Asked by fekishfaker | 18 Nov, 2023, 01:39: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Physics
A wooden block weighing 80 N rests on a rough horizontal plane, the coefficient of friction between the two being µ=0.4. If a bullet weighing 0.4 N is fired horizontally in to the block with muzzle velocity v= 500 m/s, how far will the block be displaced from its initial position? Assume that the bullet remains inside the block.
Asked by theavengers0203 | 24 May, 2023, 08:40: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Physics
law of conservation of energy in case of freely falling body
Asked by mdowaisraza581 | 16 May, 2023, 10:06: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Physics
solve question
question image
Asked by rasjad355 | 15 Jan, 2023, 04:49: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Physics
pls solve
question image
Asked by swayamagarwal2114 | 21 Jul, 2022, 05:17: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Physics
Two block A and B each of mass m are connected by a massless spring of natural length L and spring constant k. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length as shown in fig. A third identical block C, also of mass m, moving on the floor with a speed v along the line joining A and B, and collides elastically with A. Then
question image
Asked by vishal.vini86 | 22 Apr, 2022, 12:06: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Physics
Two identical small balls A and B each of mass m connected by a light inextensible string of length l are placed on a frictionless horizontal floor. With what velocity u must the ball B be projected vertically upwards so that the ball A leaves the floor?
Asked by pratham.k | 02 Jun, 2020, 12:20: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Physics
a man drags a block through 10m on rough surface (mew=0.5). A force of root3 kN acting at 30 to the horizontal . the work done by applied force is
Asked by Vedantshinde4may | 25 Feb, 2019, 05:10: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×