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3. The answer is B. (2) only.
(1) Since rail A and rail B have different inclinations, so, the velocity of the marble along the plane of the rail are different. As velocity is a vector, which has both magnitude and direction. Hence this is wrong.
(2) When it reaches the bottom, the speeds are the same. Hence the kinetic energy is the same.
(3) It undergoes different accelerations in two situations. For the same distance travelled, the time required is not the same.
4. The answer is D. 17.0 ms-1
By Newton's 2nd law of motion,
f = ma
-0.65mg = ma
a = -0.65(10) = -6.5 ms-2
By v2 = u2 + 2as
0 = u2 + 2(-6.5)(22.3)
u = 17.0 ms-1
21. The answer is B. 1200 W
Energy consumed
= 24 / 600 X (3.6 X 106)
= 144 000 J
Hence, power = 144 000 / (2 X 60) = 1200 W
28. The answer is A. (Butin fact the question is badly designed, because acceleration can bothbe +ve or -ve. If option D is whether v1 is always greater or smallerthan v2 depends on the direction of acceleration of the car, I willchoose D.)
As the car is moving with uniform acceleration, its speed must increases with time.
Hence,if we consider a journey from A to B. The time required to travel fromA to mid-way of AB, it must be larger than that of from the mid-way toB.
And for front half of the journey time, the distance travelled by the car must be smaller than half the way of AB.
That means v2 must occur later than v1, in which v2 is larger than v1.
29. The answer is B.
Consider the vertical component:
2Tcosx = W
Since x < 60*
Hence, cosx > 1/2
So, W > 2T(1/2)
W > T
Now, Tcosx = W/2
Since cosx < 1
So, T > W/2
So, W > T > W/2