Multiple Choice QuestionsThe position x of a particle with respect to time t along x- axis is given by x = 9t2 -t3 where x is in meter and t in second. What will be the position of this particle when it achieves maximum speed along the +x direction?
32 m
54 m
81 m
81 m
B.
54 m
At the instant when speed is maximum, its acceleration is zero.
Given, the position x of particle with respect to time t along x- axis
x = 9t2-t3 ... (i)
differentiating Eq. (i) with respect to time, we get speed, ie, 
Again differentiating Eq. (ii) with respect to time, we get acceleration, ie, 
Now, when speed of particle is maximum, its acceleration is zero, ie,
a= 0
18-6t = 0 or t = 3s
Putting in eq (i) We, obtain the position of a particle at that time.
x = 9 (3)2 - (3)3 = 9 (9) -27
= 81-27 = 54 m
Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at a temperature to C, the power received by a unit surface (normal to the incident rays) at a distance R from the centre of the sun is :
A particle starting from the origin (0,0) moves in a straight line in the (x,y) plane. Its coordinates at a later time are ( 
). The path of the particle makes with the x -axis an angle of:
30o
45o C
60o C
60o C
A Wheel has an angular acceleration of 3.0 rad/s2 and an initial angular speed of 2.00 rad/s. In a time of 2s it has rotated thorough an angle (in radian) of:
6
10
12
12
A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml2/3, the initial angular acceleration of the rod will be:
2g/3l
mgl/2
3gl/2
3gl/2
A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is:
A block B is pushed momentarily along a horizontal surface with an initial velocity v. if μ is the coefficient of sliding friction between B and the surface, block B will come to rest after a time:
v/gμ
gμ/v
g/v
g/v
A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is B, then: 
LA > LB
LA = LB
the relationship between LA and LB depends upon the slope of the line AB
the relationship between LA and LB depends upon the slope of the line AB
Two satellites of earth S1 and S2, are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statement is true?
The time period of S1 is four times that of S2
The potential energies of earth and satellite in the two cases are equal
S1 and S2 are moving with the same speed
S1 and S2 are moving with the same speed
Dimensions of resistance in an electrical circuit, in terms of the dimension of mass M, of length L, of time T and of current I, would be:
[ML2T-3I-1]
[ML2T-2]
[ML2T-1I-1]
[ML2T-1I-1]
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