A body of moment of inertia of 3 kg ×m^2 rotating with an angular speed of 2 rad / sec has the

Name: Problem 44, Chapter 7: Objective Physics for NEET
Uploaded: 2021-09-11T02:15:52-08:00
Duration: 1 min 11 s
Channel: Dheeraj Sharma
Description: A body of moment of inertia of 3 kg ×m^2 rotating with an angular speed of 2 rad / sec has the same KE as a mass of 12 kg moving with a speed of (a) 2 m / s (b) 1 m / s (c) 4 m / s (d) 8 m / s

step 1 In this question we have to find the linear speed of a body whose kinetic energy is same as the

Question

A body of moment of inertia of $3 \mathrm{~kg} \times \mathrm{m}^{2}$ rotating with an angular speed of $2 \mathrm{rad} / \mathrm{sec}$ has the same $\mathrm{KE}$ as a mass of $12 \mathrm{~kg}$ moving with a speed of (a) $2 \mathrm{~m} / \mathrm{s}$ (b) $1 \mathrm{~m} / \mathrm{s}$ (c) $4 \mathrm{~m} / \mathrm{s}$ (d) $8 \mathrm{~m} / \mathrm{s}$

   A body of moment of inertia of $3 \mathrm{~kg} \times \mathrm{m}^{2}$ rotating with an angular speed of $2 \mathrm{rad} / \mathrm{sec}$ has the same $\mathrm{KE}$ as a mass of $12 \mathrm{~kg}$ moving with a speed of
(a) $2 \mathrm{~m} / \mathrm{s}$
(b) $1 \mathrm{~m} / \mathrm{s}$
(c) $4 \mathrm{~m} / \mathrm{s}$
(d) $8 \mathrm{~m} / \mathrm{s}$

Objective Physics for NEET

Abhay Kumar 1st Edition

Chapter 7, Problem 44

Instant Answer

Solved by Expert Dheeraj Sharma

09/11/2021

Step 1

The formula for kinetic energy in rotation is $\frac{1}{2}I\omega^{2}$ and for linear motion is $\frac{1}{2}mv^{2}$. Show more…

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A body of moment of inertia of $3 \mathrm{~kg} \times \mathrm{m}^{2}$ rotating with an angular speed of $2 \mathrm{rad} / \mathrm{sec}$ has the same $\mathrm{KE}$ as a mass of $12 \mathrm{~kg}$ moving with a speed of (a) $2 \mathrm{~m} / \mathrm{s}$ (b) $1 \mathrm{~m} / \mathrm{s}$ (c) $4 \mathrm{~m} / \mathrm{s}$ (d) $8 \mathrm{~m} / \mathrm{s}$

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Key Concepts

Rotational Kinetic Energy

Rotational kinetic energy is the energy an object has due to its rotation, calculated using the formula ½ I ?², where I is the moment of inertia and ? is the angular speed. This concept helps in understanding how energy is stored in rotational motion.

Translational Kinetic Energy

Translational kinetic energy is the energy possessed by an object due to its linear motion, given by the equation ½ m v², where m is the mass and v is the velocity. It is a fundamental concept in mechanics for analyzing moving bodies.

Equating Kinetic Energies

Equating kinetic energies involves setting the rotational kinetic energy equal to the translational kinetic energy to find unknown quantities such as speed or angular velocity. This method is important when comparing energy across different modes of motion.

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