**Problem Statement:**A particle is located at the position vector **r** = (6.00i + 7.00j) m, and a force exerted on it is given by **F** = (4.00i + 3.00j) N.**Questions and Solutions:**(a) **What is the torque acting on the particle about the origin?**\[\boldsymbol{\tau} = -10k \, \text{N} \cdot \text{m}\]**Explanation:** The torque \(\boldsymbol{\tau}\) is calculated using the cross product of the position vector \(\mathbf{r}\) and the force vector \(\mathbf{F}\). The result is \(-10k \, \text{N} \cdot \text{m}\), indicating the direction of the torque is in the negative k direction.(b) **Can there be another point about which the torque caused by this force on this particle will be in the opposite direction and half as large in magnitude?**- Yes (Correct choice)(c) **Can there be more than one such point?**- Yes (Correct choice)(d) **Can such a point lie on the y-axis?**- Yes (Correct choice)(e) **Can more than one such point lie on the y-axis?**- No (Correct choice)(f) **Determine the position vector of one such point. (Give a point on the y-axis.)**\[\mathbf{r} = 3.3j \, \text{m}\]**Explanation:** The given answer is incorrect as indicated by the red cross. The position vector \(\mathbf{r}\) provided doesn't satisfy the conditions required for the torque to be opposite in direction and half as large.**Note:** The question involves understanding the concepts of torque, position vector, point of application, and equilibrium in physics. The cross product helps determine the torque vector, and the analysis involves vector components and properties.

f) torque = R ×F where R is the position vector of force F is the force vector 5 K^ = (y j^) × (4 i^ + 3j^)5 k^ = - 4yk^y = - 1.25 mtherefore, position vector of such point is : r = 0 i^ -1.25 j^ + 0 K^ or r = <0,-1.25,0> m

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(a) What is the torque acting on the particle about the origin? T = -10k N.m (b) Can there be another point about which the torque caused by this force on this particle will be in the opposite direction and half as large in magnitude? Yes No (c) Can there be more than one such point? Yes No (d) Can such a point lie on the y-axis? Yes No (e) Can more than one such point lie on the y-axis? Yes No (f) Determine the position vector of one such point. (Give a point on the y-axis.) r= 3.3j m

(a) What is the torque acting on the particle about the origin? T = -10k N.m (b) Can there be another point about which the torque caused by this force on this particle will be in the opposite direction and half as large in magnitude? Yes No (c) Can there be more than one such point? Yes No (d) Can such a point lie on the y-axis? Yes No (e) Can more than one such point lie on the y-axis? Yes No (f) Determine the position vector of one such point. (Give a point on the y-axis.) r= 3.3j m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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