Three blocks A, B and C are lying on a smooth | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the initial velocity of block $A$ be $v$. Since the collisions are perfectly inelastic,the blocks stick together after each collision.$1$. Col

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) Let the initial velocity of block $A$ be $v$. Since the collisions are perfectly inelastic,the blocks stick together after each collision.$1$. Collision between $A$ and $B$:By conservation of linear momentum: $mv = (m + m)v_1 = 2mv_1 \implies v_1 = v/2$.$2$. Collision between the combined mass $(A+B)$ and $C$:By conservation of linear momentum: $(2m)v_1 = (2m + M)v_f$.Substituting $v_1 = v/2$: $(2m)(v/2) = (2m + M)v_f \implies mv = (2m + M)v_f \implies v_f = \frac{mv}{2m + M}$.$3$. Kinetic Energy Analysis:Initial kinetic energy $K_i = \frac{1}{2}mv^2$.Final kinetic energy $K_f = \frac{1}{2}(2m + M)v_f^2 = \frac{1}{2}(2m + M) \left( \frac{mv}{2m + M} \right)^2 = \frac{m^2v^2}{2(2m + M)}$.Given that $5/6^{th}$ of the initial kinetic energy is lost,the final kinetic energy is $1/6^{th}$ of the initial kinetic energy:$K_f = \frac{1}{6} K_i \implies \frac{m^2v^2}{2(2m + M)} = \frac{1}{6} \left( \frac{1}{2}mv^2 \right)$.Simplifying: $\frac{m}{2m + M} = \frac{1}{6} \implies 6m = 2m + M \implies M = 4m \implies M/m = 4$.

Similar Questions

$A$ ball moving with speed $v$ hits another identical ball at rest. The two balls stick together after the collision. If the specific heat of the material of the balls is $S$,the temperature rise resulting from the collision is

If a rubber ball falls from a height $h$ and rebounds up to a height of $h/2$,the percentage loss of total energy of the initial system and the velocity of the ball just before it strikes the ground,respectively,are:

$A$ car travelling at a speed of $30 \, km/h$ is brought to a halt in $8 \, m$ by applying brakes. If the same car is travelling at $60 \, km/h$,it can be brought to a halt with the same braking force in ............... $m$.

Equal force $F (> mg)$ is applied to the string in all the $3$ cases. Starting from rest,the point of application of force moves a distance of $2 \ m$ down in all cases. In which case does the block have maximum kinetic energy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module