The position x of a particle with respect to time t along x- axis is given by x = 9t^{2} -t^{3} 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
Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at a temperature t^{o} 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:
30^{o}
45^{o} C
60^{o} C
60^{o} C
A Wheel has an angular acceleration of 3.0 rad/s^{2} 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 ml^{2}/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 v_{u} and returns to Y with a uniform speed v_{d}. 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 L_{A} when it is at A and L_{B} when it is B, then:
L_{A} > L_{B}
L_{A} = L_{B}
the relationship between L_{A} and L_{B} depends upon the slope of the line AB
the relationship between L_{A} and L_{B} depends upon the slope of the line AB
Two satellites of earth S_{1} and S_{2}, are moving in the same orbit. The mass of S_{1} is four times the mass of S_{2}. Which one of the following statement is true?
The time period of S_{1} is four times that of S_{2}
The potential energies of earth and satellite in the two cases are equal
S_{1} and S_{2} are moving with the same speed
S_{1} and S_{2} 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:
[ML^{2}T^{-3}I^{-1}]
[ML^{2}T^{-2}]
[ML^{2}T^{-1}I^{-1}]
[ML^{2}T^{-1}I^{-1}]