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

MCQ

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 $M/m$ ?

A
$5$
B
$2$
✓
$4$
D
$3$

✓

Answer

Correct option: C.

$4$

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

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

Similar questions

A block of ice with mass $m$ falls into a lake. After impact, a mass of ice $m/5$ melts. Both the block of ice and the lake have a temperature of $^o C$. If $L$ represents the heat of fusion, the minimum distance the ice fell before striking the surface is

Consider the situation shown in figure. Water $\left( {{\mu _w} = \frac{4}{3}} \right)$ is filled in a breaker upto a height of $10 \,cm$. A plane mirror fixed at a height of $5\, cm$ from the surface of water. Distance of image from the mirror after reflection from it of an object $O$ at the bottom of the beaker is......$cm$

In a radioactive substance at $t = 0$, the number of atoms is $8 \times {10^4}$. Its half life period is $3$ years. The number of atoms $1 \times {10^4}$ will remain after interval ...........$years$

A certain mass of gas at $273 K$ is expanded to $81$ times its volume under adiabatic condition. If $\gamma = 1.25$ for the gas, then its final temperature is ..... $^oC$

In the given figure the total charge stored in the combination of capacitors is $100\,\mu C$. The value of ' $x$ ' is $............$.

A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle $60^{\circ}$ with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is $(2-\sqrt{3}) / \sqrt{10} \mathrm{~s}$, then the height of the top of the inclined plane, in metres, is. . . . . . Take $g=10 \mathrm{~m} \mathrm{~s}^{-2}$.

An aluminum rod (Young's modulus $ = 7 \times {10^9}\,N/{m^2})$ has a breaking strain of $0.2\%$. The minimum cross-sectional area of the rod in order to support a load of ${10^4}$Newton's is

A man balances himself in a horizontal position by pushing his hands and feet against two parallel walls. His centre of mass lies midway between the walls. The coefficients of friction at the walls are equal. Which of the following is not correct?

A straight rod of mass $m$ and length $L$ is suspended from the identical spring as shown in the figure. The spring stretched by a distance of $x_0$ due to the weight of the wire. The circuit has total resistance $R\Omega$ . When the magnetic field perpendicular to the plane of the paper is switched on, springs are observed to extend further by the same distance. The magnetic field strength is

A tangent galvanometer has a coil of $25$ $turns$ and radius of $15 \,cm.$ The horizontal component of the earth’s magnetic field is $3 × 10^{-5}$ $T$. The current required to produce a deflection of $45^o$ in it, is.....$A$