A particle of mass m moving with velocity 1 m s- 1 collides perfectly elastically with another stationary particle of mass 2 m . If the incident particle is deflected by 90°. The heavy mass will make an angle θ with the initial direction of m equal to

Question

A particle of mass m moving with velocity 1 m s- 1 collides perfectly elastically with another stationary particle of mass 2 m . If the incident particle is deflected by 90°. The heavy mass will make an angle θ with the initial direction of m equal to (A) 60o (B) 45o (C) 15o (D) 30o

Tardigrade Admin · Accepted Answer

Conservation of momentum in initial direction of motion of

m

(let

x -

direction)

(m \times 1) \hat{i} = (2 m v) \hat{i}

v_{x} = (\frac{1}{2}) \hat{i} m s^{- 1}

0 = (m v) \hat{j} + (2 m v_{y}) \hat{j}

v_{y} = - \frac{v}{2}

K E_{B e f ore} = K E_{A f t er}

\frac{1}{2} m (1)^{2} + 0 = \frac{1}{2} m v^{2} + \frac{1}{2} 2 m (v_{x}^{2} + v_{y}^{2})

1 = v^{2} + 2 [(\frac{1}{2})^{2} + (- \frac{v}{2})^{2}]

1 = v^{2} + \frac{1}{2} + \frac{v ^{2}}{2}

\frac{1}{2} = \frac{3 v ^{2}}{2}

v = \frac{1}{3} m s^{- 1}

Let

v

be the speed of

m

after it is deflected by

9 0^{o}

.
Conservation of momentum in perpendicular direction of motion of

m

(let

y -

direction)
As the collision is elastic therefore,

t an θ = \frac{v _{y}}{v _{x}}

t an θ = \frac{\frac{v}{2}}{\frac{1}{2}} = v

t an θ = \frac{1}{3}

θ = 3 0^{o}

Q. A particle of mass $m$ moving with velocity $1 m s^{- 1}$ collides perfectly elastically with another stationary particle of mass $2 m$ . If the incident particle is deflected by $90°.$ The heavy mass will make an angle $θ$ with the initial direction of $m$ equal to

$6 0^{o}$

$4 5^{o}$

$1 5^{o}$

$3 0^{o}$

Q. A particle of mass m moving with velocity 1ms−1 collides perfectly elastically with another stationary particle of mass 2m . If the incident particle is deflected by 90°. The heavy mass will make an angle θ with the initial direction of m equal to

60o

45o

15o

30o

Q. A particle of mass $m$ moving with velocity $1 m s^{- 1}$ collides perfectly elastically with another stationary particle of mass $2 m$ . If the incident particle is deflected by $90°.$ The heavy mass will make an angle $θ$ with the initial direction of $m$ equal to

$6 0^{o}$

$4 5^{o}$

$1 5^{o}$

$3 0^{o}$