A particle moves in the x-y plane under the action of force F⃗ such that the value of its linear

Name: Problem 95, Chapter 1: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-10T04:03:48-08:00
Duration: 1 min 53 s
Channel: Akshaya Rs
Description: A particle moves in the x-y plane under the action of force F⃗ such that the value of its linear momentum 2 at any instant is p=2(cost î+sint ĵ). The angle θbetween F and p is (A) 60^∘ (B) 45^∘ (C) 30^∘ (D) 90^∘

step 1 In this question we will learn about some basic concept of the vectors. The question is a partic

Question

A particle moves in the $x-y$ plane under the action of force $\vec{F}$ such that the value of its linear momentum 2 at any instant is $p=2(\cos t \hat{i}+\sin t \hat{j})$. The angle $\theta$ between $F$ and $p$ is (A) $60^{\circ}$ (B) $45^{\circ}$ (C) $30^{\circ}$ (D) $90^{\circ}$

   A particle moves in the $x-y$ plane under the action of force $\vec{F}$ such that the value of its linear momentum 2 at any instant is $p=2(\cos t \hat{i}+\sin t \hat{j})$. The angle $\theta$
between $F$ and $p$ is
(A) $60^{\circ}$
(B) $45^{\circ}$
(C) $30^{\circ}$
(D) $90^{\circ}$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 1, Problem 95

Instant Answer

Solved by Expert Akshaya Rs

10/10/2021

Step 1

We know that force $\vec{F}$ is given by the rate of change of momentum, i.e., $\vec{F} = \frac{d\vec{p}}{dt}$. Show more…

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A particle moves in the $x-y$ plane under the action of force $\vec{F}$ such that the value of its linear momentum 2 at any instant is $p=2(\cos t \hat{i}+\sin t \hat{j})$. The angle $\theta$ between $F$ and $p$ is (A) $60^{\circ}$ (B) $45^{\circ}$ (C) $30^{\circ}$ (D) $90^{\circ}$

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Key Concepts

Linear Momentum

Linear momentum is a fundamental vector quantity in mechanics defined as the product of an object's mass and its velocity. It plays a central role in describing the motion of objects and is directly influenced by the forces acting on them.

Force as the Rate of Change of Momentum

According to Newton's second law, force is defined as the rate of change of momentum with respect to time. This principle connects dynamics to kinematics and is essential for analyzing how forces alter the motion of particles in various situations.

Vector Operations and the Dot Product

The dot product is a key vector operation that allows the determination of the angle between two vectors. It provides a method to relate the magnitudes of vectors to the cosine of the angle between them, which is essential when analyzing the directional relationships between quantities such as force and momentum.

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