Question

62 A ball rolls down an inclined plane such that the distance
(in centimeters) that it rolls in seconds is given by
s(t) = 2t^3 +3t^2 + 4 for 0 <t<3 (see figure).
(a) Find the velocity of the ball at t = 2.
(b) At what time is the velocity 30 cm/sec?
Exercise 6.2
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Answer 1

Step-by-step explanation:

Force acting on the ball is same in both the cases, therefore acceleration will also be same a

1

=a

2

. Thus, (ii) is wrong.

S=Ut+

2

at

2

Initially ball is at rest, U=0

S=

2

at

2

So, we see that: S∝t

2

Now, as the distance travelled by the two balls are S

1

sinθ=h and S

2

sinθ=2h

S

2

S

1

=

2

1

S

2

=2S

1

So, we get: t

2

=

2

t

1

Thus (i) is wrong.

The acceleration in both cases i.e at position P as well as Q is g, acting in vertically downward direction. Thus (ii) is also wrong.

Now by Conservation of Energy formula, the potential energy possessed by the ball is converted to its Kinetic energy at the bottom of the inclined plane.

PE at point Q = mg(2h) ; PE at point P = mg(h)

Thus, KE at O (when ball falls from Q) = KE at O (when ball falls from P)

So, (iii) is correct.

Answer 2

Answer:

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