(D) Using the law of conservation of energy between point $A$ and point $B$:$E_A = E_B$$\frac{1}{2}mv_A^2 + mgh = \frac{1}{2}mv_B^2$$v_B = \sqrt{v_A^2

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(D) Using the law of conservation of energy between point $A$ and point $B$:$E_A = E_B$$\frac{1}{2}mv_A^2 + mgh = \frac{1}{2}mv_B^2$$v_B = \sqrt{v_A^2 + 2gh}$Given $v_A = 5\,m/s$,$g = 10\,m/s^2$,and $h = 10\,m$:$v_B = \sqrt{5^2 + 2 \times 10 \times 10} = \sqrt{25 + 200} = \sqrt{225} = 15\,m/s$At point $B$,the particle is at a distance $r = a = 10\,m$ from point $O$. The velocity vector at $B$ is perpendicular to the radius $OB$.The angular momentum $L$ about $O$ is given by:$L = m \cdot v_B \cdot r$$L = (20 \times 10^{-3}\,kg) \times (15\,m/s) \times (10\,m)$$L = 0.02 \times 150 = 3\,kg \cdot m^2/s$.

Class 11 Physics Work, Energy and Power Work Energy Theorem and Conservation of Mechanical Energy

Medium

$A$ particle of mass $20\,g$ is released with an initial velocity $5\,m/s$ along the curve from the point $A,$ as shown in the figure. The point $A$ is at height $h = 10\,m$ from point $B.$ The particle slides along the frictionless surface. When the particle reaches point $B,$ its angular momentum about $O$ will be ......... $kg \cdot m^2/s$. [Take $g = 10\,m/s^2$]

JEE MAIN 2019 All JEE MAIN

A
$2$
B
$8$
C
$6$
D
$3$

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Work, Energy and Power

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Work Energy Theorem and Conservation of Mechanical Energy

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$A$ mass of $2 \ kg$, initially at a height of $1.2 \ m$ above an uncompressed spring with spring constant $2 \times 10^4 \ N/m$, is released from rest to fall on the spring. Taking the acceleration due to gravity as $10 \ m/s^2$ and neglecting air resistance, the compression of the spring in $mm$ is:

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$A$ simple pendulum is released from point $A$ as shown in the figure. If $m$ and $l$ represent the mass of the bob and the length of the pendulum respectively,the gain in kinetic energy at point $B$ is:

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$A$ ball of mass $300 g$ is dropped from a height $10 m$ above a sandy ground. On reaching the ground,it penetrates through a distance $1.5 m$ in sand and finally stops. The average resistance offered by the sand to oppose the motion is (acceleration due to gravity $= 10 m s^{-2}$) (in $N$)

MediumAP EAMCET 2022

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Correct the following sentence: 'System cannot possess mechanical energy but possesses work.'

Difficult

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$A$ block of mass $1\,kg$ slides on a rough horizontal surface. If the speed of the block decreases from $10\,m/s$ to $8\,m/s$,the thermal energy developed in this process is .................. $J$.

Medium

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$A$ simple pendulum is released from point $A$ as shown in the figure. If $m$ and $l$ represent the mass of the bob and the length of the pendulum respectively,the gain in kinetic energy at point $B$ is:

$A$ ball of mass $300 g$ is dropped from a height $10 m$ above a sandy ground. On reaching the ground,it penetrates through a distance $1.5 m$ in sand and finally stops. The average resistance offered by the sand to oppose the motion is (acceleration due to gravity $= 10 m s^{-2}$) (in $N$)

Correct the following sentence: 'System cannot possess mechanical energy but possesses work.'

$A$ block of mass $1\,kg$ slides on a rough horizontal surface. If the speed of the block decreases from $10\,m/s$ to $8\,m/s$,the thermal energy developed in this process is .................. $J$.

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