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QUESTION: 1

A ball is thrown vertically upward. At the highest point in its path, which of the following statements is correct?

Solution:

Until and unless the velocity of any object comes to zero, any peek in its displacement-time graph can’t be achieved. Which means for the height to be maximised the velocity must become zero. And any time of this motion the acceleration is always a constant downward due to gravity.

QUESTION: 2

A body of mass 1kg and 10kg are dropped simultaneously from the top of a tower. The ratio of the time taken by them to reach the ground is

Solution:

When an object is thrown from a height a continuous gravitational acceleration acts upon the body and hence time of flight can written equal to√2gs when we consider initial velocity to be zero. Now as we can see even if initial velocity is not zero, time of flight does not depend upon the mass of the body. Hence the time of flight is always the same ideally.

QUESTION: 3

A uniform force of (3 i + j) N acts on a particle of mass 2 kg. Hence the particle is displaced from position (2 i + k) m to position ( 4 i + 3 j - k) m. The work done by the force on the particle is,

Solution:

Uniform force acting = 3i + j N

Displacement done = (4-2)i + 3j + (-1-1)k

= 2i + 3j -2k

Thus total work done = F.s (dot product here)

We get W = 3 x 2 + 1 x 3 + 0 x -2

= 9J

QUESTION: 4

The angular velocity (in rad/s) of a body rotating at N r.p.m. is

Solution:

Angular velocity is defined as the rate of change of angular displacement with respect to time. It is usually expressed by a Greek letter ω (omega).

Mathematically, angular velocity,

ω =dθ/dt

If a body is rotating at the rate of N r.p.m. (revolutions per minute), then its angular velocity,

ω = 2πΝ / 60 rad/s

QUESTION: 5

The kinematic equation of motion v = u+at is not applicable if :

Solution:

Because if acceleration is not constant then it becomes non intertial frame. Thus this equations are only use when acceleration is constant intertial frame

QUESTION: 6

Rain falls at a speed of 50m/s and a child walks on a straight road from east to west at a speed of 100m/s. To find the direction in which the child should hold the umbrella use

Solution:

The child should hold the umbrella in the direction at which the rain appears to fall on him, which is the direction of relative speed of rain with respect to the child.

QUESTION: 7

Which of the following quantity does not remain constant during the uniform circular motion?

Solution:

- Linear momentum is not constant but angular momentum is
- Speed has to be constant for “uniform” circular motion
- For obvious reasons ω is constant
- And the same goes for α

QUESTION: 8

Two stones of different masses are thrown vertically upward with same initial velocity. Which one will rise to a greater height ?

Solution:

If we write the equation of motion for both the masses and derive a simple equation to find the maximum vertical height let say H, we get for any particle for some mass m,

H = v^{2} / 2a

Where a is gravitational acceleration and v is vertical speed. Thus as H does not depend upon m, we get both particles would have equal maximum height.

QUESTION: 9

The motion of a freely falling body is an example of:

Solution:

A freely falling body observes a constant downwards force of gravity which hence applies a constant downward acceleration upon the body.

QUESTION: 10

The position of a particle is given by x = at^{3} where a is a constant. Find the velocity as a function of time.

Solution:

We know that velocity is the first derivative of change in displacement wrt time, hence we get

V = 3at^{2}

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