Question

which of the following statements is wrong about a ball thrown vertically up (a) It is moving with constant acceleration (b) It may have different velocities at the same position (c) It may have two positions at the same time (d) The angular momentum of the particle about origin remains conserved​

Answer 1

Explanation:

Let us consider a ball projected at an angle θ with respect to horizontal x-axis with the initial velocity u .

The point O is called the point of projection, θ is the angle of projection and OB = horizontal range. The total time taken by the particle from reaching O to B is called the time of flight.

Now,

(a). The total time of flight is

Resultant displacement is zero in Vertical direction.

Therefore, by using equation of motion

s=ut−

2

1

gt

2

gt=2sinθ

t=

g

2sinθ

(b). The horizontal range is

Horizontal range OA = horizontal component of velocity × total flight time

R=ucosθ×

g

2usinθ

R=

g

u

2

sin2θ

(c). The maximum height is

It is the highest point of the trajectory point A. When the ball is at point A, the vertical component of the velocity will be zero.

By using equation of motion

v

2

=u

2

−2as

0=u

2

sin

2

θ−2gH

H=

2g

u

2

sin

2

θ

Hence, this is the required solution

Answer 2

Explanation 1

" It is moving with constant acceleration ".

• True, because, in the vertical motion of the body, the projectile has velocity 0 m/s at the highest point of the projectile.

• The force acting on the mass here, is the gravitational force and hence, the constant acceleration acting on the mass is the acceleration due to gravity $(g)$.

• Throughout the motion of the body from the ground to top and back to ground the only force or external factor acting on the body is constant the acceleration due to gravity $(9.8m/s^{2} )$.

Explanation 2

" It may have different velocities at the same position".

• True, we know, velocity is given by displacement made by the body in a given interval of time.
• A ball thrown upwards, retraces it own path in the downward motion. The only factor is the direction of the motion changes.
• Let's say while going upwards, the displacement is $+a$ , the displacement while coming downwards will be $-a$.
• Hence, the velocities while going up and down are different as velocity is a vector quantity and changes on change in the direction.

Explanation 3

" It may have two positions at the same time ".

• False. As, we know, distance is given by speed × time and for two positions at same time to be equal, the speed's at the two positions should be equal which is not possible.
• Unless, it is in projectile motion, where there are two components of velocity, horizontal and vertical.
• While talking about 1-Dimensional motion, speed is purely depended upon the distance and distance is positive always.
• Hence, the given assertion is not true.

Explanation 4

"The angular momentum of the particle about origin remains conserved".

• True, For a particle in motion, if no external force acts on it, the momentum of the particle shall remain conserved.
• We know, momentum of any body is given by $F.dt$ ( F- force ). Since, we have been given that no external force acts on the particle hence the change in momentum is 0 or the momentum stays conserved.