If A = 2i^ + 3j^ + 8k^ is

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 Multiple Choice QuestionsMultiple Choice Questions

91.

A particle is projected with a velocity v so that its horizontal range twice the greatest height attained. The horizontal range is

  • 4v25 g

  • v2g

  • v22g

  • 2v23 g


92.

Three projectiles A, B and C are projected at an angle of 30°, 45°, 60° respectively. If RA, RB and RC are ranges of A, B and C respectively, then (velocity of projection is same for A, B and C)

  • RA = RB = RC

  • RA = RC > RB

  • RA < RB < RC

  • RA = RC < RB


93.

The component ofa vector r along X-axis will have a maximum value, if

  • r is along positive X-axis

  • r is along positive Y-axis

  • r is along negative Y-axis

  • r makes an angle of 45° with the X-axis


94.

Maximum acceleration of the train in which a 50 kg box lying on its floor will remain stationary (Given, coefficient of static friction between the box and the train's floor is 0.3 and g = 10 ms-2)

  • 5.0 ms-2

  • 3.0 ms-2

  • 1.5 ms-2

  • 15 ms-2


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95.

Three bodies a ring (R), a solid cylinder (C) and a solid sphere (S) having same mass and same radius roll down the inclined plane without slipping. They start from rest, if vR, vC and vS are velocities of respective bodies on reaching the bottom of the plane, then

  • vR = vC = vS

  • vR > vC > vS

  • vR < vC < vS

  • vR = vC > vS


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96.

If A = 2i^ + 3j^ + 8k^ is perpendicular to B = 4j^ - 4i^ + αk^, then the value of α is

  • - 12

  • 12

  • 1

  • − 1


A.

- 12

Given,

A = 2i^ + 3j^ + 8k^B = 4j^ - 4i^ + αk^   = - 4i^ + 4j^ + αk^A  B, hence A . B  = 0 2i^ + 3j^ + 8k^ -4i^ + 4j^ + αk^ = 0 - 8 + 12 + 8α = 0               8α + 4 = 0                       8α = - 4                         α = - 48                         α = - 12


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97.

The angle between velocity and acceleration of a particle describing uniform circular motion is

  • 180°

  • 90°

  • 45°

  • 60°


98.

A very large number of balls are thrown vertically upwards in quick successions in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is 5 m, the number of balls thrown per minute is (take g = 10 m/s2)

  • 80

  • 120

  • 40

  • 60


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99.

A projectile is moving at 20 ms-1 at its highest point, where it breaks into equal parts due to an internal explosion. One part moves vertically up at 30 ms-1 with respect to the ground. Then the other part will move at

  • 20 ms-1

  • 1031 ms-1

  • 50 ms-1

  • 30 ms-1


100.

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

  • R/2

  • R/3

  • R/5

  • R/4


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