(A) By the law of conservation of momentum,the initial momentum is zero,so $m_1 v_1 + m_2 v_2 = 0$,which implies $v_1 / v_2 = -m_2 / m_1$.When the car

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(A) By the law of conservation of momentum,the initial momentum is zero,so $m_1 v_1 + m_2 v_2 = 0$,which implies $v_1 / v_2 = -m_2 / m_1$.When the carts stop,their kinetic energy is dissipated by the work done against friction: $\frac{1}{2} m v^2 = \mu m g S$.This gives $S = \frac{v^2}{2 \mu g}$.Therefore,the ratio of distances traveled is $\frac{S_1}{S_2} = \frac{v_1^2}{v_2^2} = \left( \frac{m_2}{m_1} \right)^2$.Substituting the given values: $\frac{18}{S_2} = \left( \frac{300}{100} \right)^2 = 3^2 = 9$.Thus,$S_2 = \frac{18}{9} = 2 \ m$.

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

Medium

Two carts are pushed apart by the explosion of a charge placed between them. $A$ cart of mass $100 \ kg$ stops after traveling a distance of $18 \ m$. What distance will a cart of mass $300 \ kg$ travel before stopping? The coefficient of friction $\mu$ between the carts and the ground is the same for both.

A
$2$
B
$0.8$
C
$4$
D
$5.2$

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Class 11

Physics Questions

Chapter

Newton's Laws of Motion and Friction

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Mix Examples-Newton's Laws of Motion and Friction

$A$ $0.5\, kg$ ball moving with a speed of $12\, m/s$ strikes a hard wall at an angle of $30^\circ$ with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for $0.25\, s$,the average force acting on the wall is ........... $N$.

MediumAIPMT 2006

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$A$ plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^o$,the box starts to slip and slides $4.0\, m$ down the plank in $4.0\, s$. The coefficients of static and kinetic friction between the box and the plank will be,respectively:

DifficultAIPMT 2015

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Calculate the acceleration (in $m/s^{2}$) of the block and trolley system shown in the figure. The coefficient of kinetic friction between the trolley and the surface is $0.05$. (Given: $g = 10\; m/s^{2}$,mass of the string is negligible and no other friction exists).

MediumNEET 2020

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Match the items in Column-$I$ with those in Column-$II$.

Column-$I$ Column-$II$

$(1)$ Newton's third law of motion $(a)$ $\vec{F}_{12} = -\vec{F}_{21}$

$(2)$ Law of conservation of momentum $(b)$ $\Delta \vec{p} = 0$

$(c)$ $\vec{F}_{12} = \vec{F}_{21}$

Column-$I$	Column-$II$
$(1)$ Newton's third law of motion	$(a)$ $\vec{F}_{12} = -\vec{F}_{21}$
$(2)$ Law of conservation of momentum	$(b)$ $\Delta \vec{p} = 0$
	$(c)$ $\vec{F}_{12} = \vec{F}_{21}$

Easy

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The system shown in the figure is in equilibrium and at rest. The spring and string are massless. Now,the string is cut. The acceleration of mass $2m$ and $m$ just after the string is cut will be:

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$A$ $0.5\, kg$ ball moving with a speed of $12\, m/s$ strikes a hard wall at an angle of $30^\circ$ with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for $0.25\, s$,the average force acting on the wall is ........... $N$.

Calculate the acceleration (in $m/s^{2}$) of the block and trolley system shown in the figure. The coefficient of kinetic friction between the trolley and the surface is $0.05$. (Given: $g = 10\; m/s^{2}$,mass of the string is negligible and no other friction exists).

Match the items in Column-$I$ with those in Column-$II$. Column-$I$ Column-$II$ $(1)$ Newton's third law of motion $(a)$ $\vec{F}_{12} = -\vec{F}_{21}$ $(2)$ Law of conservation of momentum $(b)$ $\Delta \vec{p} = 0$ $(c)$ $\vec{F}_{12} = \vec{F}_{21}$

The system shown in the figure is in equilibrium and at rest. The spring and string are massless. Now,the string is cut. The acceleration of mass $2m$ and $m$ just after the string is cut will be:

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Match the items in Column-$I$ with those in Column-$II$.

Column-$I$ Column-$II$

$(1)$ Newton's third law of motion $(a)$ $\vec{F}_{12} = -\vec{F}_{21}$

$(2)$ Law of conservation of momentum $(b)$ $\Delta \vec{p} = 0$

$(c)$ $\vec{F}_{12} = \vec{F}_{21}$