A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure correctly shown the displacementtime curve for its motion?
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As given that power constant
As we know that power
As the body is moving unidirectionally.
Hence,
constant constant by question
Displacement
Verifies the graph (b).
Which of the diagrams shown in figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit?
Which of the diagrams shown in figure represents variation of total mechanical energy of a pendulum oscillating in air as function of time?
A mass of is moving along a circular path of radius 1 . If the mass moves with , its kinetic energy would be
0
As given that, mass revolution Radius
linear speed
So, verifies the option (a).
A raindrop falling from a height above ground, attains a near terminal velocity when it has fallen through a height . Which of the diagrams shown in figure correctly shows the change in kinetic and potential energy of the drop during its fall up to the ground?
P.E. is maximum when drop start falling at as it fall is P.E. decrease gradually to zero. So, it rejects the graph (a), (c) and (d).
K.E. at is zero as drop falls with zero velocity, its velocity increases (gradually), hence, first also increases. After sometime speed (velocity) is constant thisis called terminal velocity, so, also become constant. It happens when it falls height or remains at from ground, then PE decreases continuously as the drop is falling continuously.
The variation in PE and KE is best represented by (b).
In a shotput event an athlete throws the shotput of mass with an initial speed of at from a height 1.5 above ground. Assuming air resistance to be negligible and acceleration due to gravity to be , the kinetic energy of the shotput when it just reaches the ground will be
As given that, By the law of conservation of mechanical energy as no force acts on shotput after thrown.
Total energy when it reaches ground, so
.
Which of the diagrams in figure correctly shows the change in kinetic energy of an iron sphere falling freely in a lake having sufficient depth to impart it a terminal velocity?
First velocity of the iron sphere
after sometime its velocity becomes constant, called terminal velocity. Hence, according first increases and then becomes constant due to resistance of sphere and water which is represented by (b).
A cricket ball of mass moving with a speed of hits at the middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remain in contact for , the force that the batsman had to apply to hold the bat firmly at its place would be
As given that,
time of contact
So, final velocity is acc. to initial force applied by batsman.
So, change in momentum of the ball
As we know that, force
Hence negative sign shown that direction of force will be opposite to initial velocity which taken positive direction. Hence verify the option (c).
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