Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 602

A meter stick of mass \(400 \mathrm{gm}\) is pivoted at one end and displaced through an angle 600 the increase in its P.E. is \(\overline{\\{\mathrm{A}\\} 2}\) \(\\{B\\} 3\) \(\\{\) C \(\\}\) Zero \(\\{\mathrm{D}\\} 1\)

Short Answer

Expert verified
The increase in potential energy of the meter stick is approximately 1.703 J, which is closest to \(\overline{\mathrm{A}} 2\).

Step by step solution

01

Convert mass to kg and angle to radians

Firstly, convert the mass of the meter stick from grams to kilograms: \( mass = \dfrac{400~\mathrm{grams}}{1000} = 0.4 ~\mathrm{kg} \) Now convert the angle of displacement from 60 degrees to radians: \( \theta = 60^\circ * \frac{\pi}{180^\circ} = \frac{\pi}{3} ~\mathrm{radians} \)
02

Calculate the change in height

We need to find out the change in height of the meter stick's center of mass due to pivoting. When it is horizontal, the center of mass is right at the middle of the stick (0.5 meters). When it pivots, it moves upwards to form a 30-60-90 degree triangle. The height of the triangle is given by: \( h = 0.5 \times \sin{(\pi/3)} \)
03

Calculate the increase in potential energy

To find the increase in potential energy (ΔP.E.), we need to multiply the mass, gravitational acceleration (g = 9.81 m/s^2), and the change in height: ΔP.E. = mass × g × h ΔP.E. = 0.4 × 9.81 × (0.5 × \(\sin{(π/3)}\)) ΔP.E. ≈ 1.703 J (approx)
04

Choose the correct option

Now that we have calculated the increase in potential energy (ΔP.E.), we can choose the correct option among the given choices. The answer is closest to 2, so the correct option is: \(\overline{\mathrm{A}} 2\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A solid cylinder of mass \(\mathrm{M}\) and radius \(\mathrm{R}\) rolls down an inclined plane of height \(\mathrm{h}\). The angular velocity of the cylinder when it reaches the bottom of the plane will be. \(\\{\mathrm{A}\\}(2 / \mathrm{R}) \sqrt{(\mathrm{gh})}\) \(\\{\mathrm{B}\\}(2 / \mathrm{R}) \sqrt{(\mathrm{gh} / 2)}\) \(\\{\mathrm{C}\\}(2 / \mathrm{R}) \sqrt{(\mathrm{gh} / 3)}\) \(\\{\mathrm{D}\\}(1 / 2 \mathrm{R}) \sqrt{(\mathrm{gh})}\)

A solid sphere and a solid cylinder having same mass and radius roll down the same incline the ratio of their acceleration will be.... \(\\{\mathrm{A}\\} 15: 14\) \(\\{\mathrm{B}\\} 14: 15\) \(\\{\mathrm{C}\\} 5: 3\) \(\\{\mathrm{D}\\} 3: 5\)

A circular disc \(\mathrm{x}\) of radius \(\mathrm{R}\) is made from an iron plate of thickness \(t\). and another disc \(Y\) of radius \(4 R\) is made from an iron plate of thickness \(t / 4\) then the rotation between the moment of inertia \(\mathrm{I}_{\mathrm{x}}\) and \(\mathrm{I}_{\mathrm{y}}\) is \(\\{\mathrm{A}\\} \mathrm{I}_{\mathrm{y}}=64 \mathrm{I}_{\mathrm{x}}\) \(\\{B\\} I_{y}=32 I_{x}\) \(\\{\mathrm{C}\\} \mathrm{I}_{\mathrm{y}}=16 \mathrm{I}_{\mathrm{x}}\) \(\\{\mathrm{D}\\} \mathrm{I}_{\mathrm{y}}=\mathrm{I}_{\mathrm{x}}\)

Two blocks of masses \(10 \mathrm{~kg}\) an \(4 \mathrm{~kg}\) are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives velocity of \(14 \mathrm{~m} / \mathrm{s}\) to the heavier block in the direction of the lighter block. The velocity of the centre of mass is : \(\\{\mathrm{A}\\} 30 \mathrm{~m} / \mathrm{s}\) \(\\{\mathrm{B}\\} 20 \mathrm{~m} / \mathrm{s}\) \(\\{\mathrm{C}\\} 10 \mathrm{~m} / \mathrm{s}\) \(\\{\mathrm{D}\\} 5 \mathrm{~m} / \mathrm{s}\)

If distance of the earth becomes three times that of the present distance from the sun then number of days in one year will be .... \(\\{\mathrm{A}\\}[365 \times 3]\) \(\\{\mathrm{B}\\}[365 \times 27]\) \(\\{\mathrm{C}\\}[365 \times(3 \sqrt{3})]\) \(\\{\mathrm{D}\\}[365 /(3 \sqrt{3})]\)
See all solutions

Recommended explanations on English Textbooks

Language Analysis

Read Explanation

Global English

Read Explanation

Morphology

Read Explanation

Linguistic Terms

Read Explanation

Listening and Speaking

Read Explanation

Lexis and Semantics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free