(C) Since the surface is smooth,mechanical energy is conserved throughout the motion.Let the initial height be $h_1 = 100 \, m$ and the final height b

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) Since the surface is smooth,mechanical energy is conserved throughout the motion.Let the initial height be $h_1 = 100 \, m$ and the final height be $h_2 = 20 \, m$.The initial velocity $u = 0 \, m/s$.According to the law of conservation of energy:$PE_{initial} + KE_{initial} = PE_{final} + KE_{final}$$mgh_1 + 0 = mgh_2 + \frac{1}{2}mv^2$$mg(h_1 - h_2) = \frac{1}{2}mv^2$$v = \sqrt{2g(h_1 - h_2)}$Substituting the values $(g = 10 \, m/s^2)$:$v = \sqrt{2 \times 10 \times (100 - 20)}$$v = \sqrt{20 \times 80}$$v = \sqrt{1600}$$v = 40 \, m/s$.

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

Medium

$A$ spherical ball of mass $20 \, kg$ is stationary at the top of a hill of height $100 \, m$. It slides down a smooth surface to the ground,then climbs up another hill of height $30 \, m$ and finally slides down to a horizontal base at a height of $20 \, m$ above the ground. The velocity attained by the ball is ............... $m/s$.

AIEEE 2005 All AIEEE

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

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Work, Energy, Power and Collision

Subtopic

Work Energy Theorem and Conservation of Mechanical Energy

Previous Year

AIEEE 2005 Paper All AIEEE years →

$A$ small sphere of mass $m$ and radius $r$ slides down the smooth surface of a large hemispherical bowl of radius $R$. If the sphere starts sliding from rest, the total kinetic energy of the sphere at the lowest point $A$ of the bowl will be [given, moment of inertia of sphere $= \frac{2}{5} mr^2$].

EasyWBJEE 2024

View Solution

$A$ smooth semicircular tube $AB$ of radius $R$ is fixed in a vertical plane and contains a heavy flexible chain of length $\pi R$. Find the velocity $v$ with which it will emerge from the open end $B$ of the tube,when slightly displaced.

Difficult

View Solution

The total work done on a particle is equal to the change in its kinetic energy. This is applicable:

Easy

View Solution

As shown in the figure,a particle of mass $10 \ kg$ is placed at a point $A$. When the particle is slightly displaced to its right,it starts moving and reaches the point $B$. The speed of the particle at $B$ is $x \ m/s$. (Take $g = 10 \ m/s^2$). The value of $x$ to the nearest integer is:

MediumJEE MAIN 2021

View Solution

An unloaded bus can be stopped by applying brakes on a straight road after covering a distance $x$. Suppose the passengers add $50 \%$ of its weight as the load and the braking force remains unchanged,how far will the bus go after the application of the brakes? (Velocity of the bus in both cases is the same.)

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

$A$ smooth semicircular tube $AB$ of radius $R$ is fixed in a vertical plane and contains a heavy flexible chain of length $\pi R$. Find the velocity $v$ with which it will emerge from the open end $B$ of the tube,when slightly displaced.

The total work done on a particle is equal to the change in its kinetic energy. This is applicable:

As shown in the figure,a particle of mass $10 \ kg$ is placed at a point $A$. When the particle is slightly displaced to its right,it starts moving and reaches the point $B$. The speed of the particle at $B$ is $x \ m/s$. (Take $g = 10 \ m/s^2$). The value of $x$ to the nearest integer is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module