A  particle of mass m is released from rest and follows a parabolic path is shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?


D.

Potential V (x) versus x is parabolic, SHM starts from an extreme position and x versus t should be a cosin curve.

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A missile is fired at maximum range with an initial velocity of 20 m/s. If g =10 m/s2 the range of the missile is 

  • 50 m

  • 60 m

  • 20 m

  • 20 m


C.

20 m

For maximum range of projectile, θ will be 45o by the law of projectile motion


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A body is moving with velocity 30 m/s towards east. After 10 s its velocity becomes 40 m/s towards the north. The average acceleration of the body is 

  • 7 m/s2

  • square root of 7 space m divided by s squared
  • 5 m/s2

  • 5 m/s2


C.

5 m/s2

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A projectile is fired an angle of 45o with the horizontal.Elevation angle of the projectile at the highest point as seen from the point of projection is 

  • 60o

  • tan-1(1/2)

  • tan to the power of negative 1 end exponent space open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses
  • tan to the power of negative 1 end exponent space open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses


B.

tan-1(1/2)


Height of projectile

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Two particles A and B, move with constant velocities v1 and v2. At the initial moment, their position vectors are r1 and r2 respectively. The condition for particles A and B for their collision is 

  • fraction numerator straight r subscript 1 space equals space straight r subscript 2 over denominator vertical line straight r subscript 1 minus straight r subscript 2 vertical line end fraction space equals space fraction numerator v subscript 2 space equals space v subscript 1 over denominator vertical line v subscript 2 minus v subscript 1 vertical line end fraction
  • r1.v1 = r2.v2

  • r1 x v1 = r2 x v2

  • r1 x v1 = r2 x v2


A.

fraction numerator straight r subscript 1 space equals space straight r subscript 2 over denominator vertical line straight r subscript 1 minus straight r subscript 2 vertical line end fraction space equals space fraction numerator v subscript 2 space equals space v subscript 1 over denominator vertical line v subscript 2 minus v subscript 1 vertical line end fraction

For two particles A and B moves with constant velocitites v1 and v2, such that two particles to collide, the direction of the relative velocity of one with respect to other should be directed towards the relative position of the other particle.i.e., direction of relative position of 1 w.r.t

similarly, » direction of velocity of 2 w.r.t 1
so, for collision of A and B, we get


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