(A) $1$. Conservation of linear momentum during the perfectly inelastic collision:$m_b u = (m_b + m_B) v$$0.1 \times 20 = (0.1 + 1.9) v$$2 = 2v \Right

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(A) $1$. Conservation of linear momentum during the perfectly inelastic collision:$m_b u = (m_b + m_B) v$$0.1 \times 20 = (0.1 + 1.9) v$$2 = 2v \Rightarrow v = 1\, m/s$$2$. Conservation of mechanical energy for the combined system falling from height $h = 1\, m$:$KE_f = PE_i + KE_i$$KE_f = mgh + \frac{1}{2} m v^2$$KE_f = (2)(10)(1) + \frac{1}{2}(2)(1)^2$$KE_f = 20 + 1 = 21\, J$

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

Medium

$A$ block of mass $1.9\, kg$ is at rest at the edge of a table of height $1\, m$. $A$ bullet of mass $0.1\, kg$ collides with the block and sticks to it. If the velocity of the bullet is $20\, m/s$ in the horizontal direction just before the collision,then the kinetic energy just before the combined system strikes the floor is $....J$. (Take $g = 10\, m/s^2$. Assume there is no rotational motion and loss of energy after the collision is negligible.)

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$21$
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$23$
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$19$
D
$20$

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Mix Examples-Work, Energy, Power and Collision

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Fill in the blanks:
$(a)$ If the momentum of an object is doubled,its kinetic energy becomes ........
$(b)$ For a perfectly inelastic collision,the coefficient of restitution $e$ $=$ .....
$(c)$ An appliance with $1\,kW$ power consumes $1\,kWh$ of energy in ....... time.

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$A$ bob $B$ of mass $m$ at rest is hanging vertically from the ceiling via a massless string of length $10 \text{ m}$. $A$ point mass $A$ of mass $m$ travelling horizontally with speed $10 \text{ ms}^{-1}$ hits bob $B$ elastically. The bob $B$ rises $h$ meters after the collision. Taking the acceleration due to gravity $g = 10 \text{ ms}^{-2}$ and neglecting the size of the bob, the value of $h$ is:

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The rate of doing work by a force acting on a particle moving along the $x$-axis depends on the position $x$ of the particle and is equal to $2x$. The velocity of the particle is given by the expression:

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$A$ particle is moving in a circle of radius $r$ under the action of a force $F = \alpha r^2$ which is directed towards the centre of the circle. The total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy $= 0$ for $r = 0$).

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Which of the following graphs correctly represents the relationship between kinetic energy $(E)$,potential energy $(U)$,and height $(h)$ from the ground for a particle moving vertically?

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Fill in the blanks:$(a)$ If the momentum of an object is doubled,its kinetic energy becomes ........ $(b)$ For a perfectly inelastic collision,the coefficient of restitution $e$ $=$ ..... $(c)$ An appliance with $1\,kW$ power consumes $1\,kWh$ of energy in ....... time.

The rate of doing work by a force acting on a particle moving along the $x$-axis depends on the position $x$ of the particle and is equal to $2x$. The velocity of the particle is given by the expression:

$A$ particle is moving in a circle of radius $r$ under the action of a force $F = \alpha r^2$ which is directed towards the centre of the circle. The total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy $= 0$ for $r = 0$).

Which of the following graphs correctly represents the relationship between kinetic energy $(E)$,potential energy $(U)$,and height $(h)$ from the ground for a particle moving vertically?

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Fill in the blanks:
$(a)$ If the momentum of an object is doubled,its kinetic energy becomes ........
$(b)$ For a perfectly inelastic collision,the coefficient of restitution $e$ $=$ .....
$(c)$ An appliance with $1\,kW$ power consumes $1\,kWh$ of energy in ....... time.