A Particle has initial velocity andleft parenthesis 3 space bold i with bold hat on top space plus 4 space bold j with bold hat on top right parenthesis has acceleration.left parenthesis 0.1 space bold i with bold hat on top space plus space 0.3 space bold j with bold hat on top right parenthesis Its speed after 10s is

  • 7 unit

  • 7 square root of 2 unit
  • 8.5 unit

  • 8.5 unit


B.

7 square root of 2 unit
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Six vectorsbold a with bold rightwards arrow on top and bold f with bold rightwards arrow on tophave the magnitudes and directions indicated in the figure. Which of the following statements is true?

  • bold b with bold rightwards arrow on top bold space bold plus bold c with bold rightwards arrow on top bold space bold equals bold space bold f with bold rightwards arrow on top
  • bold d with bold rightwards arrow on top bold space bold plus bold c with bold rightwards arrow on top bold space bold equals bold space bold f with bold rightwards arrow on top
  • stack bold d bold space with bold rightwards arrow on top bold space bold plus bold space bold e with bold rightwards arrow on top bold space bold equals bold space bold f with bold rightwards arrow on top
  • stack bold d bold space with bold rightwards arrow on top bold space bold plus bold space bold e with bold rightwards arrow on top bold space bold equals bold space bold f with bold rightwards arrow on top

C.

stack bold d bold space with bold rightwards arrow on top bold space bold plus bold space bold e with bold rightwards arrow on top bold space bold equals bold space bold f with bold rightwards arrow on top

If two non -zero vectors are represented by the two adjacent sides of a parallelogram, then the resultant is given by the diagonal of the parallelogram passing through the point of intersection of the two vectors

therefore, 

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A particle moves a distance x in time t according to equation x  = (t +5)-1. The acceleration of particle is proportional to

  • (velocity)3/2

  • (distance)2

  • (distance)-2

  • (distance)-2


A.

(velocity)3/2

Given, distance x = ( t + 5)-1   ...... (i)

Differentiating eq. (i) w.r.t, we get

 

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The speed of the projectile at its maximum height is half of its initial speed. The angle of projection is

  • 60o

  • 15o

  • 30o

  • 30o


A.

60o

The speed of projectile at its maximum height

v' = vo cos θ

vo/2 = vo cos θ

cos θ = 1/2

θ = 60o

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Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be

  • 2v

  • 0

  • 1.5 v

  • 1.5 v


B.

0

As initially, both the particles were at rest, therefore, velocity of the centre of mass was zero and there is no external force on the system so the speed of the centre of mass remains constant i.e, it should be equal to zero.

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