Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JIPMER 2016
Exam
JIPMER
Year
2016
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

JIPMER 2016 · Physics · Center of Mass, Momentum and Collision

A sphere of mass m moving with velocity v hits inelastically with...

A sphere of mass mm moving with velocity vv hits inelastically with another stationary sphere of same mass. The ratio of their final velocities will be (in terms of ee )

Options

  1. Av1v2=1+e1−e\frac{v_1}{v_2}=\frac{1+e}{1-e}
  2. Bv1v2=1−e1+e\frac{v_1}{v_2}=\frac{1-e}{1+e}
  3. Cv1v2=1+e2\frac{v_1}{v_2}=\frac{1+e}{2}
  4. Dv1v2=1−e2\frac{v_1}{v_2}=\frac{1-e}{2}

Correct answer

B. v1v2=1−e1+e\frac{v_1}{v_2}=\frac{1-e}{1+e}

Step-by-step solution

As coefficient of restitution, e=v2−v1u1−u2=v2−v1u−0⇒v2−v1=eue=\frac{v_2-v_1}{u_1-u_2}=\frac{v_2-v_1}{u-0} \Rightarrow \quad v_2-v_1=e u...(i) By conservation of momentum, Momentum before collision = Momentum after collision mu=mv1+mv2⇒v1+v2=u\begin{aligned} & m u=m v_1+m v_2 \\ & \Rightarrow \quad v_1+v_2=u \\ & \end{aligned}...(ii) On solving Eqs. (i) and (ii), we get v1=u2(1−e) and v2=u2(1+e)∴v1v2=1−e1+e\begin{aligned} & v_1=\frac{u}{2}(1-e) \text{ and } v_2=\frac{u}{2}(1+e) \\ & \therefore \quad \frac{v_1}{v_2}=\frac{1-e}{1+e} \\ & \end{aligned}
Practice Center of Mass, Momentum and Collision on Quantrex Academy →

More from Center of Mass, Momentum and Collision

A frictionless circular wire of unit radius is fixed on the horizontal plane. Two point… NEET 2026Bob B of mass m at rest is hanging vertically from the ceiling via a massless string of… NEET 2026A ball of mass 0.5 kg is dropped from a height of 40 m . The ball hits the ground and… NEET 2025Two bodies A and B of same mass undergo completely inelastic one dimensional collision.… NEET 2024Two particles A and B initially at rest, move towards each other under mutual force of… NEET 2023A 1 ~kg object strikes a wall with velocity 1 ~ms^ -1 at an angle of 60^ ∘ with the wall… NEET 2023A bullet of mass m hits a block of mass M elastically. The transfer of energy is the… NEET 2023A shell of mass m is at rest initially. It explodes into three fragments having mass in… NEET 2022 Full Center of Mass, Momentum and Collision list All JIPMER PYQs