Question

A particle of mass m strikes a wall with speed v at an angle ${{30}^{0}}$ with the wall elasticity as shown in the figure. The magnitude of impulse imparted the ball by the wall is
A) $mv$
B) $\dfrac{mv}{2}$
C) $2mv$
D) $\sqrt{3}mv$

Answer 1

Hint: Speed is defined as the distance covered per unit time and speed is a scalar quantity. SI unit of speed is $m{{s}^{-1}}$ . Displacement is defined as the process in which objects' positions are changed and in displacement the initial position of objects are changed. Displacement is also defined as change in initial position of objects to the final position and displacement is denoted as S.

Complete step-by-step solution:
Velocity is defined as the rate of change of displacement with respect to time and in kinematics velocity is a fundamental concept.SI unit of velocity is $m{{s}^{-1}}$ velocity tracking is the measure of velocity.
Velocity (v) =$\dfrac{\Delta S}{\Delta t}$
Momentum is defined as the product of the mass and velocity of objects. Momentum is a vector quantity which has both magnitude and direction. Momentum (p) =mv and the dimensional formula of momentum is\[ML{{T}^{-1}}\]. The SI unit of momentum is kilogram meter per second$(kgm{{s}^{-1}})$ and momentum is a conserved quantity.
Linear momentum perpendicular to the wall before the particle strike is given by :
$p=mv\sin ({{30}^{0}})=\dfrac{mv}{2}$
Linear momentum which acts along the wall before the particle strike is given by :
$p=mv\cos ({{30}^{0}})$
Linear momentum perpendicular to the wall after particle strike is given by :
$p=-mv\sin ({{30}^{0}})=-\dfrac{mv}{2}$
Linear momentum which acts along the wall before the particle strike is given by:
$p=mv\cos {{({{30}^{0}})}^{{}}}$
Impulse which is equal to change in linear momentum.
Impulse = Change in linear momentum
Linear momentum which will change when it is perpendicular to the wall
Therefore $Impulse=-\dfrac{mv}{2}-\dfrac{mv}{2}=-mv$
The magnitude of impulse is equal to $mv$
So the correct option is A.

Note: The dimensional formula of displacement is ${{M}^{0}}{{L}^{1}}{{T}^{0}}$ and displacement plays a very important role while determining velocity (v). Velocity is also a vector quantity. Displacement plays a very important role while determining velocity (v). Displacement is a vector quantity which has both magnitude and direction and displacement is measured in terms of meters.