The displacement of particle is given by x = &alph

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 Multiple Choice QuestionsMultiple Choice Questions

111.

A police jeep is chasing with velocity of 45 km/h. A thief in another jeep moving with velocity 153 km/h. Police fires a bullet with muzzle velocity of 180 m/s. The velocity it will strike the car of the thief is

  • 150 m/s

  • 27 m/s

  • 450 m/s

  • 250 m/s


112.

Two similar charges having mass m and 2m are placed in an electric field. The ratio of their kinetic energy is :

  • 4:1

  • 1:1

  • 2:1

  • 1:2


113.

A car starts from rest, moves with an acceleration a and then decelerates at a constant rate b for sometimes to come to rest. If the total time taken is t. The maximum velocity of car is given by :

  • a b ta + b 

  • a2 ta + b

  • a ta+ b

  • b2 ta+b


114.

A river is flowing from west to east with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so, as to take the shortest possible path to go to the south?

  • 30o east of south

  • 60o east of south

  • 60o west of south

  • 30o west of north


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115.

Two boys are standing at the ends A and B of a ground, where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1 The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is 

  • av2 + v12

  • a2ν2  - ν12

  • aν -  ν1

  • aν + ν1


116.

A ball is thrown vertically upward. It has a speed of 10 m/s when it has reached one-half of its maximum height. How high does the ball rise? ( Take, g = 10 m/s2 )

  • 15 m

  • 10 m

  • 20 m

  • 5 m


117.

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

  • 2 νd νuνd + νu

  • vu vd

  • vd vuvd + vu

  • vu + vd2


118.

A particle moves along a straight line OX. At a time t (in second) the distance x ( in metre ) of the particle from O is given by x = 40 + 12 t - t3 . How long would the particle travel before coming to rest?

  • 24 m

  • 40 m

  • 56 m

  • 16 m


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119.

A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc?

  • 0.4 cm

  • 2.4 cm

  • 1.8 cm

  • 1.2 cm


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120.

The displacement of particle is given by x = αo+ α1t2 - α2t23 .What is its acceleration?

  • 2α23

  • -2α23

  • α2

  • Zero


B.

-2α23

Acceleration is the rate of change of velocity and velocity is the rate of change of displacement.
The displacement equation is given by

              x = αo + α1 t2 - α2 t23

Veiocity = rate of change of displacement

                  v = dxdt     = ddtαo + α1 t2 - α2 t23 

                    ν  =  0 + α12-2 α2t3v   =  α1 2 - 2 α2t3

Acceleration = rate of change of velocity

                      α = dvdtα = ddtα12 - 2α23tα = 0 - 2α23α = - 2α23


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