A particle of mass 100 g moving at an initial speed u collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes 0.2 J after the collision, what could be the minimum and the maximum value of u?
A particle of mass 100 g moving at an initial speed u collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes 0.2 J after the collision, what could be the minimum and the maximum value of u?
The correct option is B
mass of particle = 0.1 kg
Total K.E. after the collision = 0.2 J
As the zero energy is lost in the case of perfectly elastic collision, and in the case of perfectly elastic
collision of two similar bodies, their velocities are exchanged.
So, 12mu2 = 0.2
u = 2 m/s {This is the minimum speed required to get the given K.E.}
Now for maximum velocity, we take the collision to be perfectly inelastic as maximum energy is lost in this type.
According to conservation of linear momentum
mu+m(0)=(m+m)vmu=2mvu=2vv=u2Total energy=12(2m)v2=0.2J=mv2=0.2mu24=0.2u2=(0.2)(4)100×10−3=8u=√8=2√2m/s
mass of particle = 0.1 kg
Total K.E. after the collision = 0.2 J
As the zero energy is lost in the case of perfectly elastic collision, and in the case of perfectly elastic
collision of two similar bodies, their velocities are exchanged.
So, 12mu2 = 0.2
u = 2 m/s {This is the minimum speed required to get the given K.E.}
Now for maximum velocity, we take the collision to be perfectly inelastic as maximum energy is lost in this type.
According to conservation of linear momentum
mu+m(0)=(m+m)vmu=2mvu=2vv=u2Total energy=12(2m)v2=0.2J=mv2=0.2mu24=0.2u2=(0.2)(4)100×10−3=8u=√8=2√2m/s