These questions consists of two statements each printed as Assertion and Reason. While answering these question you are required to choose any one of the following five reponses
(a) If both Assertion and Reason arecorrect and Reason is the correct explanation of Asserrtion.
(b) If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
(c ) If Assertion is true but Reason is false.
(d) If Assertion is false but Reason is true.
Assertion At any instant the magnitude of rate of change of potential energy of the projectile of mass 1 kg is numerically equal to magnitude of a.v (where a is acceleration due to gravity and v is velocity at that instant)
Reason The graph representing power delivered by the gravitational force acting on the projectile with time will be straight line with negative slope.

Answer

C

Explanation

(c ) Assertion `(dU)/(dt)=(d)/(dt)(mgh)="mg"(d)/(dt)(u_(y)t-(1)/(2)"gt"^(2))`
`=mg(u_(y)-"gt")=mgv_(y)`
`:. " " |(dU)/(dt)|=mg|v_(y)|`
For `" "` m=1kg
`|(dU)/(dt)|=g(u_(y)-"gt")" " ……..(i)`
`a.v=(-ghatj).[u_(x)hati+(u_(y)-"gt")hatj]`
`=-g(u_(y)-"gt")=g|v_(y)|" " .....(ii)`
From Eqs. (i) and (ii) we can see that two magnitudes are equal.
Reason `P=F.v=(-mghatj).[v_(x)hati+(u_(y)-"gt")hatj]`
`=-mgu_(y)+mg^(2)t`
So, P versus t graph has the positive slope.