OnlineCBT Logo OnlineCBT
⚲
English
OnlineCBT Logo OnlineCBT
⚲

Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

हिन्दी

Which of the following conditions is both necessary and sufficient for the centre of mass of a continuous body to coincide with its geometric centre?

  1. The body must be homogeneous and possess reflection symmetry about planes passing through its geometric centre.
  2. The body must be in pure rotational equilibrium under external forces.
  3. The body must be planar with uniform thickness only.
  4. The total external torque acting on the body must be zero.

Correct answer · Option 1

The body must be homogeneous and possess reflection symmetry about planes passing through its geometric centre.

Explanation

Due to uniform density and reflection symmetry, every element \( dm \) at \( (x,y,z) \) cancels with \( dm \) at \( (-x,-y,-z) \), making \( \int \mathbf{r} dm = 0 \) at the geometric centre.

Related questions

Given below are two statements: Statement I: The kinetic energy of a body of moment of inertia \( I \) rotating with an angular velocity \( \omega \) about a fixed axis is given by \( K = \frac{1}{2} I \omega^2 \). Statement II: The moment of inertia of a rotating rigid body changes if its angular velocity is doubled. In the light of the above statements, choose the most appropriate answer from the options given below:→Given two vectors \( \mathbf{a} = 3\hat{i} - 4\hat{j} + 5\hat{k} \) and \( \mathbf{b} = -2\hat{i} + \hat{j} - 3\hat{k} \), the cross product \( \mathbf{a} \times \mathbf{b} \) is equal to:→Consider the following statements regarding rotational motion about a fixed axis: (A) Only those components of external torques that lie along the axis of rotation can cause the body to rotate about the axis. (B) Torques perpendicular to the fixed axis are balanced by the constraint forces exerted by the hinges/supports. (C) Forces parallel to the axis of rotation produce non-zero torque about that axis. (D) The rate of work done by an external torque \( \tau \) rotating a body with angular speed \( \omega \) is given by \( P = \tau \omega \). How many of the above statements are correct?→In an L-shaped uniform lamina formed by three identical squares of side length \( b = 2\text{ m} \) as oriented in Fig. 6.11 (with bottom-left square at origin having vertices from \( (0,0) \) to \( (2,2) \)), the coordinate of the centre of mass is:→
ऑनलाइन कंप्यूटर आधारित परीक्षा

हमारा मिशन है – "विद्यार्थियों को शिक्षित करना और उन्हें प्रतिस्पर्धी परीक्षाओं की तैयारी में उनकी पूर्ण क्षमता के साथ उत्कृष्टता प्राप्त करने में सहायता करना। साथ ही उनमें अच्छे संस्कारों का संचार करना और उनके व्यक्तित्व का विकास करना।"

उपयोगी लिंक
महत्वपूर्ण पेज
कोर्सेज और अभ्यास
संपर्क करें
पता

प्लॉट नं. 10, धोलीगुमटी, पंडितपुरा रोड, बंदीकुई, दौसा (राजस्थान) – 303313

संपर्क करें

+91 7877547686

 ई-मेल

onlinecbtportal@gmail.com

 हेल्पलाइन नंबर

+91 7877547686
साझा करें
डाउनलोड करने के लिए क्लिक करें
Get it on Google Play

ऐप डाउनलोड करने
के लिए Google Play पर
उपलब्ध है

उपयोग की शर्तें | गोपनीयता नीति | कुकी नीति | अस्वीकरण | संपादकीय नीति | तथ्य जांच | सुधार | DMCA | विज्ञापन विकल्प

Copyright © 2026 - OnlineCBT.in. All Rights Reserved.

WhatsApp Chat