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 

• 24 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 :

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• 
• 
• 

D.

From Stefan's law, the rate at which energy is radiated by sun at its surface si 
P = σ x 4 πr²T⁴

[Sun is a perfectly black body as it emits radiations of all wavelengths and so for it e =1]
The intensity of this power at earth's surface (under the assumption R >>r_o) 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

• 0⁰

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

• 4

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

• 3g/2l