Question:
A particle moves from position \(3\hat{i}+2\hat{j}+6\hat{k}\) to \(14\hat{i}+13\hat{j}+9\hat{k}\) due to a uniform force of \(4\hat{i}+\hat{j}+3\hat{k}\,N\) . Find the work done, if the displacement is in metre.
A particle moves from position \(3\hat{i}+2\hat{j}+6\hat{k}\) to \(14\hat{i}+13\hat{j}+9\hat{k}\) due to a uniform force of \(4\hat{i}+\hat{j}+3\hat{k}\,N\) . Find the work done, if the displacement is in metre.
Updated On: Sep 4, 2023
- 16 J
- 64 J
- 32 J
- 48 J
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct answer is B:64 J
Work done \(= F \cdot d\)
\(= (4 \hat i + \hat j + 3 \hat k) \cdot[(14 - 3) \hat i + (13 - 2) \hat k + (9 - 6) \hat k]\)
\(= (4 \hat i + \hat j + 3 \hat k)\cdot (11 \hat i + 11 \hat j + 3 \hat k)\)
\(= 44 + 11 + 9 = 64 \, J\)
Work done \(= F \cdot d\)
\(= (4 \hat i + \hat j + 3 \hat k) \cdot[(14 - 3) \hat i + (13 - 2) \hat k + (9 - 6) \hat k]\)
\(= (4 \hat i + \hat j + 3 \hat k)\cdot (11 \hat i + 11 \hat j + 3 \hat k)\)
\(= 44 + 11 + 9 = 64 \, J\)
Was this answer helpful?
0
0
Top Questions on Motion in a plane
- The resultant of two vectors \( \vec{A} \) and \( \vec{B} \) is perpendicular to \( \vec{A} \) and its magnitude is half that of \( \vec{B} \). The angle between vectors \( \vec{A} \) and \( \vec{B} \) is ________ .
- JEE Main - 2024
- Physics
- Motion in a plane
- If two vectors \(\vec{A}\) and \(\vec{B}\) having equal magnitude \(R\) are inclined at an angle \(\theta\), then
- JEE Main - 2024
- Physics
- Motion in a plane
- A ball dropped from a bridge hits the surface of the water in 3 𝑠. The height of the bridge, ignoring air resistance, is ___ 𝑚 (rounded off to one decimal place). (Use $𝑔 = 9.8 𝑚𝑠^{−2}$)
- IIT JAM BT - 2024
- Physics
- Motion in a plane
- A bullet is fired from a gun at the speed of 280 ms-1 in the direction 30° above the horizontal. The maximum height attained by the bullet is
(g = 9.8 ms-2, sin 30° = 0.5)- NEET (UG) - 2023
- Physics
- Motion in a plane
Car P is heading east with a speed V and car Q is heading north with a speed \(\sqrt{3}\). What is the velocity of car Q with respect to car P?
- KEAM - 2023
- Physics
- Motion in a plane
View More Questions
Questions Asked in JKCET exam
- A moving block having mass $m$, collides with another stationary block having mass $4\,m$. The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v$, then the value of coefficient of restitution (e) will be
- JKCET - 2019
- work, energy and power
- A force $ F = 3x^2 + 2x + 1 $ acts on a body in the $ x $ -direction. The work done by this force during a displacement from $ x = -1 $ to $ +1 $ is
- JKCET - 2019
- work, energy and power
- What is the colour of the flame on heating potassium in the flame of a Bunsen burner?
- JKCET - 2019
- GROUP 1 ELEMENTS
- If $ a $ , $ b $ , $ c $ are the lengths of three edges of unit cell, $ \alpha $ is the angle between side $ b $ and $ c $ , $ \beta $ is the angle between side $ a $ and $ c $ and $ \gamma $ is the angle between side $ a $ and $ b $ , what is the Bravais Lattice dimensions of a tetragonal crystal?
- JKCET - 2019
- The solid state
- Which of the following compounds is known as copper glance?
- JKCET - 2019
- General Principles and Processes of Isolation of Elements
View More Questions
Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration