Center of MassHard
Question
Two particles of equal mass m are projected form the ground with speed v1 and v2 at angle θ1 and θ2 as shown in figure. The centre of mass of the two particles
Options
A.will move in a parabolic path for any values of v1, v2, θ1 and θ2
B.can move in a vertical line
C.can move in a horizontal line
D.will move in a straight line for any value of v1, v2, θ1 and θ2
Solution
Centre of mass will move in a vertical line if v1 cos θ1 = v2 cos θ2. Otherwise for any other values it will follow a parabolic path.
Mathod II.
= V1 cosθ1 î + (V1 sinθ1 − gt) ĵ 
Parabolic path
= − V2 cosθ2 î + (V2 sinθ2 − gt) ĵ 
Parabolic path
= 
If
= 0 [Centre of mass of the Particle move only along Y axis ]
v1 cos θ1 − v2 cos θ2 = 0 ⇒ v1 cos θ1 = v2 cos θ2
then path may be straight line.
Mathod II.
= V1 cosθ1 î + (V1 sinθ1 − gt) ĵ Parabolic path = − V2 cosθ2 î + (V2 sinθ2 − gt) ĵ Parabolic path = If
= 0 [Centre of mass of the Particle move only along Y axis ]v1 cos θ1 − v2 cos θ2 = 0 ⇒ v1 cos θ1 = v2 cos θ2
then path may be straight line.
Create a free account to view solution
View Solution FreeMore Center of Mass Questions
A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The k...A block moving in air explodes in two parts then just after explosion (neglect change in momentum duet to gravity)...In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in figure...Two masses of 1g and 4g are moving with equal kinetic energy. The ratio of the magnitude of their linear momentum is -...Two identical particles move towards each other with velocity 2v and v respectively. The velocity of centre of mass is...