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When a particle is undergoing motion, th...

When a particle is undergoing motion, the diplacement of the particle has a magnitude that is equal to or smaller than the total distance travelled by the particle. In many cases the displacement of the particle may actually be zero, while the distance travelled by it is non-zero. Both these quantities, however depend on the frame of reference in which motion of the particle is being observed. Consider a particle which is projected in the earth's gravitational field, close to its surface, with a speed of `100sqrt(2) m//s`, at an angle of `45^(@)` with the horizontal in the eastward direction. Ignore air resistance and assume that the acceleration due to gravity is `10 m//s^(2)`.
The motion of the particle is observed in two different frames: one in the ground frame (A) and another frame (B), in which the horizontal component of the displacement is always zero. Two observers locates in these frames ill agree on :-

A

The total distance travelled by the particle

B

The horizontal range of the particle

C

The maximum height risen by the particle

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
In ground frame [A] it is simply a projectile motion. But in [B] frame horizontal component of the displacement is zero i.e. in this frame only vertical comp. appear which is responsible for the maximum height.
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When a particle is undergoing motion, the diplacement of the particle has a magnitude that is equal to or smaller than the total distance travelled by the particle. In many cases the displacement of the particle may actually be zero, while the distance travelled by it is non-zero. Both these quantities, however depend on the frame of reference in which motion of the particle is being observed. Consider a particle which is projected in the earth's gravitational field, close to its surface, with a speed of 100sqrt(2) m//s , at an angle of 45^(@) with the horizontal in the eastward direction. Ignore air resistance and assume that the acceleration due to gravity is 10 m//s^(2) . There exists a frame (D) in which the distance travelled by the particle is minimum. This minimum distance is equal to :-

When a particle is undergoing motion, the diplacement of the particle has a magnitude that is equal to or smaller than the total distance travelled by the particle. In many cases the displacement of the particle may actually be zero, while the distance travelled by it is non-zero. Both these quantities, however depend on the frame of reference in which motion of the particle is being observed. Consider a particle which is projected in the earth's gravitational field, close to its surface, with a speed of 100sqrt(2) m//s , at an angle of 45^(@) with the horizontal in the eastward direction. Ignore air resistance and assume that the acceleration due to gravity is 10 m//s^(2) . " A third observer (C) close to the surface of the reports that particle is initially travelling at a speed of 100sqrt(2) m//s making on angle of 45^(@) with the horizontal, but its horizontal motion is northward". The third observer is moving in :-

Knowledge Check

  • The displacement of a particle is given by x = (t-2)^(2) where x is in metre and t in second. The distance covered by the particle in first 4 seconds is

    A
    4m
    B
    8m
    C
    12m
    D
    16m

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