Three blocks A, B and C are lying on a smooth horizontal surface,… - Vidyadip

Question

Three blocks $A, B$ and $C$ are lying on a smooth horizontal surface, as shown in the figure. $A$ and $B$ have equal masses, $m$ while $C$ has mass $M$. Block $A$ is given an initial speed $v$ towards $B$ due to which it collides with $B$ perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically if $\frac{5}{6}^{th}$ of the initial kinetic energy is lost in whole process. What is value of $M/m$ ?

✓

Answer

c
Apply $LMC$ (Linear Momentum Conservation)

$mv = (2m + M) v'$

$v' = \frac{{mv}}{{2m + M}}$

Initial energy

$\frac{1}{2}$ $m{v^2}$

Final energy

$\frac{1}{2}\,\left( {2m + M} \right){\left( {\frac{{mv}}{{2m + M}}} \right)^2}$

$Initial\, kinetic\, energy - Final\, Kinetic\, energy =$ $\frac{5}{6}$ of initial kinetic energy.

After solving, we get, $\frac{M}{m} = 4.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

From the top of a tower, a ball is thrown vertically upward which reaches the ground in $6 \,s$. A second ball thrown vertically downward from the same position with the same speed reaches the ground in $1.5\, s$. A third ball released, from the rest from the same location, will reach the ground in........ $s$.

Two $10 \; cm$ long, straight wires, each carrying a current of $5 \; A$ are kept parallel to each other. If each wire experienced a force of $10^{-5} \; N$, then separation between the wires is $\dots \; cm$.

In a coil of resistance $8 \Omega$, the magnetic flux due to an external magnetic field varies with time as $\phi=\frac{2}{3}\left(9- t ^{2}\right)$. The value of total heat produced in the coil, till the flux becomes zero, will be $....J$

An electron moves through a uniform magnetic field $\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T$ At a particular instant of time, the velocity of electron is $\overrightarrow{ u }=3 \hat{ i }+5 \hat{ j }\ m/s.$ If the magnetic force acting on electron is $\overrightarrow{ F }=5 ekN$ , where e is the charge of electron, then the value of $B _0$ is $.........T.$

If $\vec{a}$ and $\vec{b}$ makes an angle $\cos ^{-1}\left(\frac{5}{9}\right)$ with each other, then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$ The integer value of $n$ is . . . . . . ..

Ice at $-20\,^oC$ is added to $50\,g$ of water at $40\,^oC.$ When the temperature of the mixture reaches $0\,^oC,$ it is found that $20\,g$ of ice is still unmelted. The amount of ice added to the water was close to ........$g$ (Specific heat of water $= 4.2\,J/g/^oC)$ Heat of fusion of water at $0^oC = 334\,J/g$ )

A body of mass $5\,kg$ rests on a rough horizontal surface of coefficient of friction $0.2.$ The body is pulled through a distance of $10\,m$ by a horizontal force of $25\, N$. The kinetic energy acquired by it is ......... $J$

The amplitude of an oscillating simple pendulum is $10\,cm$ and its period is $4\, sec$. Its speed after $1\, sec$ after it passes its equilibrium position, is ... $m/s$

Three different dielectrics are filled in a parallel plate capacitor as shown. What should be the dielectric constant of a material, which when fully filled between the plates produces same capacitance?

A block of mass $10\, kg$ is placed on an inclined plane. When the angle of inclination is $30°$, the block just begins to slide down the plane. The force of static friction is ....... $kg\, wt$