Embibe Experts Solutions for Chapter: Center of Mass, Momentum and Collision, Exercise 1: BITSAT 2018

A particle $X$ of mass $m$ and initial velocity $u$ collides with another particle $Y$ of mass $\frac{3m}{4}$, which is at rest. The collision is head-on and perfectly elastic. The ratio of de-Broglie wavelengths ${\lambda }_Y$ and ${\lambda }_X$ after the collision is,

The escape velocity from the surface of earth is $v_e.$ A body is projected with velocity $3v_e.$ With what constant velocity will it move in the inter planetary space?

An object of mass $5 \mathrm{kg}$ is projected with a velocity $20 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle $60°$, to the horizontal. At the highest point of its path, the projectile explodes and breaks up into two fragments of masses $1 \mathrm{kg}$ and $4 \mathrm{kg}.$ The fragments separate horizontally after the explosion, which releases internal energy such that the $KE$ of the system af the highest point is doubled. The separation between the two fragments when they reach the ground is

A trolley having mass of $200 \mathrm{kg}$ moves with uniform speed of $36 {\mathrm{kmh}}^{-1}$ on a frictionless track. A child of mass $20 \mathrm{kg}$ runs on the trolley from one end to the other ($10 \mathrm{m}$ away)  with a speed of $4 \mathrm{m} {\mathrm{s}}^{-1}$ relative to the trolley in a direction opposite to its motion and ultimately jumps out of the trolley. With how much velocity has the trolley moved from the time the child begins to run?