The 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 

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/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 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 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]