The position x of a particle with respect to time t along x- axi

Subject

Physics

Class

NEET Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

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 


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

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2.

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 :

  • fraction numerator 4 πr squared σt to the power of 4 over denominator straight R squared end fraction
  • fraction numerator straight r squared straight sigma left parenthesis straight t plus 273 right parenthesis to the power of 4 over denominator 4 πR squared end fraction
  • fraction numerator 16 space straight pi squared straight r squared σt to the power of 4 over denominator straight R squared end fraction
  • fraction numerator 16 space straight pi squared straight r squared σt to the power of 4 over denominator straight R squared end fraction
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3.

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  ( square root of 3 comma space 3). The path of the particle makes with the x -axis an angle of:

  • 30o

  • 45o C

  • 60o C

  • 60o C

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4.

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

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5.

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

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6.

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:

  • fraction numerator 2 straight v subscript straight d straight v subscript straight u over denominator straight v subscript straight d plus straight v subscript straight u end fraction
  • square root of straight v subscript straight u straight v subscript straight d end root
  • fraction numerator straight v subscript straight d straight v subscript straight d over denominator straight v subscript straight d plus straight v subscript straight u end fraction
  • fraction numerator straight v subscript straight d straight v subscript straight d over denominator straight v subscript straight d plus straight v subscript straight u end fraction
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7.

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

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8.

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

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9.

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

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10.

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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