(A) According to the law of conservation of mechanical energy,the total mechanical energy remains constant in the absence of non-conservative forces l

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(A) According to the law of conservation of mechanical energy,the total mechanical energy remains constant in the absence of non-conservative forces like friction.Initial mechanical energy at height $h_1 = 100 \ m$ is $E_i = mgh_1 + 0 = 20 \times 10 \times 100 = 20,000 \ J$.Final mechanical energy at height $h_f = 20 \ m$ is $E_f = mgh_f + \frac{1}{2}mv^2 = 20 \times 10 \times 20 + \frac{1}{2} \times 20 \times v^2 = 4,000 + 10v^2$.Equating initial and final energy: $20,000 = 4,000 + 10v^2$.$10v^2 = 16,000$.$v^2 = 1,600$.$v = 40 \ m/s$.

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

Difficult

$A$ ball of mass $20 \ kg$ is at rest on a hill of height $100 \ m$. It starts rolling down,reaches the ground,climbs another hill of height $30 \ m$,and finally rolls down to a horizontal platform at a height of $20 \ m$ from the ground. What will be its velocity at this point? (Assume $g = 10 \ m/s^2$)

A
$40$
B
$20$
C
$10$
D
$10\sqrt{30}$

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Work, Energy, Power and Collision

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Work Energy Theorem and Conservation of Mechanical Energy

$A$ car accelerates from rest to $u \ m/s$. The energy spent in this process is $E \ J$. The energy required to accelerate the car from $u \ m/s$ to $2u \ m/s$ is $nE \ J$. The value of $n$ is ..............

MediumJEE MAIN 2023

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The mass of a pendulum bob is $50 \ gm$. The bob is released from a horizontal position $A$ as shown in the figure. If the length of the pendulum is $1.5 \ m$,what will be its kinetic energy when it reaches the lowest point $B$ of its path? (Take $g = 10 \ m/s^2$)

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$A$ body of mass $0.5\, kg$ travels on a straight-line path with velocity $v = (3x^2 + 4)\, m/s$. The net work done by the force during its displacement from $x = 0$ to $x = 2\, m$ is $.......J$.

MediumJEE MAIN 2022

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$A$ body of mass $1 \text{ kg}$ moves along a straight line with a velocity $v = 2x^2$. The work done by the body during displacement from $x = 0$ to $5 \text{ m}$ is . . . . . . $J$.

DifficultJEE MAIN 2026

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$A$ particle of mass $m$ moves with a velocity $v = a\sqrt{x}$,where $a$ is a constant and $x$ is the displacement. Find the total work done by all forces during the displacement from $x = 0$ to $x = d$.

Medium

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The mass of a pendulum bob is $50 \ gm$. The bob is released from a horizontal position $A$ as shown in the figure. If the length of the pendulum is $1.5 \ m$,what will be its kinetic energy when it reaches the lowest point $B$ of its path? (Take $g = 10 \ m/s^2$)

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