(B) According to the Law of Conservation of Linear Momentum $(COLM)$:$mv + 0 = m(v/2) + MV'$$mv/2 = MV'$$V' = mv / (2M)$Here,$V'$ is the velocity acqu

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(B) According to the Law of Conservation of Linear Momentum $(COLM)$:$mv + 0 = m(v/2) + MV'$$mv/2 = MV'$$V' = mv / (2M)$Here,$V'$ is the velocity acquired by the block of mass $M$ immediately after the bullet passes through it.Using the Law of Conservation of Mechanical Energy $(COME)$ for the block:$(1/2)MV'^2 = MgH$Substitute $V' = mv / (2M)$ into the equation:$(1/2)M(mv / 2M)^2 = MgH$$(1/2)M(m^2v^2 / 4M^2) = MgH$$m^2v^2 / (8M^2) = MgH$$H = m^2v^2 / (8M^2g)$

Class 11 Physics Work, Energy, Power and Collision Mix Examples-Work, Energy, Power and Collision

Difficult

$A$ wooden block of mass $M$ is suspended by a cord and is at rest. $A$ bullet of mass $m$,moving with a velocity $v$,passes through the block and emerges with a velocity $v/2$ in the same direction. If the block rises to a height $H$,calculate the value of $H$.

A
$m^2v^2/2M^2g$
B
$m^2v^2/8M^2g$
C
$mv^2/4Mg$
D
$mv^2/2Mg$

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Class 11

Physics Questions

Chapter

Work, Energy, Power and Collision

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Mix Examples-Work, Energy, Power and Collision

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

Column-$I$ Column-$II$

$(1)$ Work done is zero $(a)$ By gravitational force (when body moves down)

$(2)$ Work done is positive $(b)$ Against gravitational force (when body moves up)

$(3)$ Work done is negative $(c)$ By centripetal force

Column-$I$	Column-$II$
$(1)$ Work done is zero	$(a)$ By gravitational force (when body moves down)
$(2)$ Work done is positive	$(b)$ Against gravitational force (when body moves up)
$(3)$ Work done is negative	$(c)$ By centripetal force

Medium

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$A$ block moving horizontally on a smooth surface with a speed of $40 \, m/s$ splits into two equal parts. If one of the parts moves at $60 \, m/s$ in the same direction,then the fractional change in the kinetic energy will be $x: 4$ where $x = ..... .$

DifficultJEE MAIN 2021

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Name the instrument used to measure the coefficient of restitution of a material and explain why frictional force is a non-conservative force.

Easy

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$A$ $2 \, kg$ block is placed on a frictionless inclined plane with an angle of $30^\circ$ and a length of $2 \, m$. After reaching the bottom of the incline,it travels on a surface with a coefficient of friction of $0.25$. What distance (in $m$) will it travel on the surface before coming to rest?

Difficult

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$A$ circular well of diameter $2 \ m$ has water up to the ground level. If the bottom of the well is at a depth of $14 \ m$,the time taken in seconds to empty the well using a $1.4 \ kW$ motor is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

MediumAP EAMCET 2025

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$A$ wooden block of mass $M$ is suspended by a cord and is at rest. $A$ bullet of mass $m$,moving with a velocity $v$,passes through the block and emerges with a velocity $v/2$ in the same direction. If the block rises to a height $H$,calculate the value of $H$.

Similar Questions

Match the items in Column-$I$ with Column-$II$. Column-$I$ Column-$II$ $(1)$ Work done is zero $(a)$ By gravitational force (when body moves down) $(2)$ Work done is positive $(b)$ Against gravitational force (when body moves up) $(3)$ Work done is negative $(c)$ By centripetal force

$A$ block moving horizontally on a smooth surface with a speed of $40 \, m/s$ splits into two equal parts. If one of the parts moves at $60 \, m/s$ in the same direction,then the fractional change in the kinetic energy will be $x: 4$ where $x = ..... .$

Name the instrument used to measure the coefficient of restitution of a material and explain why frictional force is a non-conservative force.

$A$ $2 \, kg$ block is placed on a frictionless inclined plane with an angle of $30^\circ$ and a length of $2 \, m$. After reaching the bottom of the incline,it travels on a surface with a coefficient of friction of $0.25$. What distance (in $m$) will it travel on the surface before coming to rest?

$A$ circular well of diameter $2 \ m$ has water up to the ground level. If the bottom of the well is at a depth of $14 \ m$,the time taken in seconds to empty the well using a $1.4 \ kW$ motor is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

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

Column-$I$ Column-$II$

$(1)$ Work done is zero $(a)$ By gravitational force (when body moves down)

$(2)$ Work done is positive $(b)$ Against gravitational force (when body moves up)

$(3)$ Work done is negative $(c)$ By centripetal force