(D) Let $M = 10\,kg$ and $m = 0.05\,kg.$ By conservation of linear momentum during the collision:$mv = (M + m)V_0$$V_0 = \frac{mv}{M + m} = \frac{0.05

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(D) Let $M = 10\,kg$ and $m = 0.05\,kg.$ By conservation of linear momentum during the collision:$mv = (M + m)V_0$$V_0 = \frac{mv}{M + m} = \frac{0.05v}{10.05} \approx \frac{0.05v}{10} = 0.005v$The block moves a distance $s = 2\,m$ before stopping due to friction. The retardation $a$ is:$a = \mu g = 0.05 \times 10 = 0.5\,m/s^2$Using $v_f^2 - u^2 = 2as$:$0 - V_0^2 = 2(-a)s \implies V_0^2 = 2as = 2 \times 0.5 \times 2 = 2$$V_0 = \sqrt{2}\,m/s$Since $V_0 = \frac{0.05v}{10.05} \approx 0.005v$,we have $0.005v = \sqrt{2} \implies v = 200\sqrt{2}\,m/s$.For a freely falling object,$v_{final} = \sqrt{2gH}$. Given $v_{final} = \frac{v}{10} = \frac{200\sqrt{2}}{10} = 20\sqrt{2}\,m/s$:$20\sqrt{2} = \sqrt{2 \times 10 \times H}$$(20\sqrt{2})^2 = 20H$$400 \times 2 = 20H \implies 800 = 20H \implies H = 40\,m = 0.04\,km$.

Class 11 Physics Laws of Motion Mix Examples-Newton's Laws of Motion and Friction

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$A$ block of mass $M = 10\,kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $\mu = 0.05.$ When hit by a bullet of mass $m = 50\,g$ moving with speed $v,$ which gets embedded in it,the block moves and comes to a stop after moving a distance of $2\,m$ on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height $H,$ then neglecting energy losses and taking $g = 10\,m/s^2,$ the value of $H$ is close to ................. $km$.

JEE MAIN 2015 All JEE MAIN

A
$0.05$
B
$0.02$
C
$0.03$
D
$0.04$

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Laws of Motion

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Mix Examples-Newton's Laws of Motion and Friction

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Give the magnitude and direction of the net force acting on a stone of mass $0.1\; kg$,
$(a)$ just after it is dropped from the window of a stationary train,
$(b)$ just after it is dropped from the window of a train running at a constant velocity of $36\; km/h$,
$(c)$ just after it is dropped from the window of a train accelerating with $1\; m/s^2$,
$(d)$ lying on the floor of a train which is accelerating with $1\; m/s^2$,the stone being at rest relative to the train.
Neglect air resistance throughout.

Medium

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$A$ $1.0 \ kg$ block of wood sits on top of an identical block of wood,which sits on top of a flat level table made of plastic. The coefficient of static friction between the wood surfaces is $\mu_1$,and the coefficient of static friction between the wood and plastic is $\mu_2$. $A$ horizontal force $F$ is applied to the top block only,and this force is increased until the top block starts to move. The bottom block will move with the top block if and only if

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$A$ pebble of mass $0.05 \, kg$ is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble,$(a)$ during its upward motion,$(b)$ during its downward motion,$(c)$ at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of $45^{\circ}$ with the horizontal direction? Ignore air resistance.

Medium

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Statement $I :$ $A$ cyclist is moving on an unbanked road with a speed of $7 \, km/h$ and takes a sharp circular turn along a path of radius $2 \, m$ without reducing the speed. The static friction coefficient is $0.2$. The cyclist will not slip and pass the curve $(g = 9.8 \, m/s^2)$.
Statement $II :$ If the road is banked at an angle of $45^{\circ}$,the cyclist can cross the curve of $2 \, m$ radius with a speed of $18.5 \, km/h$ without slipping.

DifficultJEE MAIN 2021

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Which of the following options correctly describes the variation of the speed $v$ and acceleration $a$ of a point mass falling vertically in a viscous medium that applies a force $F = -kv$,where $k$ is a constant,on the body? (Graphs are schematic and not drawn to scale)

MediumJEE MAIN 2016

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Which of the following options correctly describes the variation of the speed $v$ and acceleration $a$ of a point mass falling vertically in a viscous medium that applies a force $F = -kv$,where $k$ is a constant,on the body? (Graphs are schematic and not drawn to scale)

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