A particle moves in a straight line with retardation proportiona

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 Multiple Choice QuestionsMultiple Choice Questions

1.

A block is kept on a frictionless inclined surface with angle of inclination α. The incline is given an acceleration a to keep the block stationary. Then a is equal to

  • g/tanα

  • g cosecα

  • g

  • g

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2.

A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function time is given by

  • fraction numerator mv squared over denominator straight T squared. end fraction straight t
  • mv squared over straight T squared. straight t squared
  • 1 half mv squared over straight T squared. straight t
  • 1 half mv squared over straight T squared. straight t
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3.

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

  • x2

  • ex

  • x

  • x


A.

x2

In this problem acceleration (a) is given in terms of displacement (x)  to determine the velocity with respect to position or displacement we have to apply integration method.
From given information a =-kx, where a is acceleration, x is displacement and k is proportionality constant. 

vdx over dx space equals space minus space kx space open square brackets therefore space dv over dt space equals space fraction numerator begin display style dv end style over denominator dx end fraction open parentheses dx over dt close parentheses space equals space straight v dv over dx close square brackets
straight v space dv space equals space minus kx space dx
Let for any displacement from 0 to x , the velocity changes from vo to v

integral subscript straight v subscript straight o end subscript superscript straight v space vdv space equals space minus integral subscript 0 superscript straight x space kx space dx
rightwards double arrow space integral subscript 0 superscript straight x space kx space dx
rightwards double arrow space fraction numerator straight v squared minus straight v subscript 0 superscript 2 over denominator 2 end fraction space equals space minus space kx squared over 2
rightwards double arrow space straight m space open parentheses fraction numerator straight v squared minus space straight v subscript 0 superscript 2 over denominator 2 end fraction close parentheses space equals space fraction numerator negative mkx squared over denominator 2 end fraction
increment straight K space proportional to space straight x squared

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4.

A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed ν0/2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

  • yes, 60°

  • yes, 30°

  • no

  • no

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5.

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.


6.

A person observes that the full length of a train subtends an angle of 15°. If the distance between the train and the person is 3 km, the length of the train, calculated using parallax method, in meters is

  • 45

  • 45 π

  • 250 π

  • 75 π


7.

The following figure gives the movement of an object. Select the correct statement from the given choices.

       

  • The total distance travelled by the object is 975 m

  • The maximum acceleration of the object is 2m/s2

  • The maximum deceleration happend between 25th and 85th seconds

  • The object was at rest between 10th and 15th seconds


8.

Two object P and Q, travelling in the same direction starts from rest. While the object P starts at time t = 0 and object Q starts later at t = 30 min. The object P has an acceleration of 40 km/h2. To catch P at a distance of 20 km, the acceleration of Q should be

  • 40 km/h2

  • 80 km/h2

  • 160 km/h2

  • 120 km/h2


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9.

A train of length L move with a constant speed Vt. A person at the back of the train fires a bullet at time t = 0 towards a target which is at a distance of D (at time t = 0) from the front of the train (on the same direction of motion). Another person at the front of the train fires another bullet at time t = T towards the same target. Both bullets reach the target at the same time. Assuming the speed of the bullets Vb are same, the length of the train is

  • T × (Vb × 2Vt)

  • T × (Vb + Vt)

  • 2VbDVb + Vt + T Vb - Vt

  • T × (Vb − 2Vt)


10.

A person from a truck, moving with a constant speed of 60 km/h, throws a ball upwards with a speed of 60 km/h. Neglecting the effect of Earth and choose the correct answer from the given choice.

  • The person cannot catch the ball when it comes down since the truck is moving

  • The person can catch the ball when it comes down, if the truck is stopped immediately after throwing the ball

  • The person can catch the ball when it comes down, if the truck continues to move with a constant speed of 60 km/h

  • The person can catch the ball when it comes down, if the truck moves with speed more than 60 km/h


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