NEETPhysicsWork, Power and Energy
Statement (I) : The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration. Statement (II) : From a height of 15 ~m a ball is projected vertically upwards with a velocity of 30 ~m / s . If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is 30 % . Statement (III) : The velocity acquired by a body of mass
Options
- AStatements I, II, III are true
- BStatements I, III are true, but statement II is false
- CStatement I is true, but statements II and III are false
- DStatements I, II are true, but statement III is false
Correct answer
C. Statement I is true, but statements II and III are false
Step-by-step solution
We have aligned & K . E = 1 2 mV ^2 & d dx ( K . E )= 1 2 m 2 ~V dV dx aligned Slope of ( K.E - x ) curve = ma a So, (I) is correct When ball just strike the ground, then V = 30^2+2 10 15 = 1200 ~m / s If ball reaches the same height after striking the ground then, velocity after collision =30 ~m / s aligned & So, E = 1 2 ~m (1200-900) & = 1 2 ~m 300 & E E 100= 1 2 ~m 300 1 2 ~m 1200 100=25 % aligned So, (II) is incorrect. Now, equation of motion are independent of mass. So velocity will not depend on mass. So (III