A particle moves under the action of a force F -2 - along a line y - x -1- If work done by the force along the path is zero- then - isA- 2B- 3C- 4D- 4 -3

The correct option is A 2W = F⃗. dr = (αî nbsp;+ 2 ĵ).(dx î + dy ĵ) W = α dx + 2 dy = 0 α dx = 2dy dy/dx = α/2 Given y + x = 1 dy/dx = 1 On comparing ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Angular Analogue of Linear Momentum

A particle mo...

Question

A particle moves under the action of a force $\to F = α^i + 2^j$ along a line y + x = 1. If work done by the force along the path is zero, then $α$ is

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 \sqrt{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2$
$W = \to F . \to d r = (α^i + 2^j) . (d x^i + d y^j) W = α d x + 2 d y = 0 α d x = - 2 d y \frac{d y}{d x} = \frac{- α}{2} G i v e n y + x = 1 \frac{d y}{d x} = - 1$
On comparing, we get
$- \frac{α}{2} = - 1 \Rightarrow α = 2$

Suggest Corrections

Similar questions

Q. A particle moves under the action of a force

\to F = 20^i + 15^j

along a straight line

3 y + α x = 5

, where

α

is a constant. If the work done by the force

F

is zero, then the value of

α

is:

Q. A force

\to F = 2^i + 3^j - 4^k

N

, acts on a particle which is constrained to move in the X-Y plane along the line

x = y

. If the particle moves

5 \sqrt{2}

m, the work done by force in joule is:

Q. A particle moves along the x-axis from

x = 0

x = 5 m

under the influence of a force

F

(in N) given by

F = 3 x^{2} - 2 x + 7

. Calculate the work done by this force

Q. An object is moving along a straight line path from P to Q under the action of a force

F = (4^i - 3^j + 2^k) N

. If the co-ordinate of P & Q in metres are (3, 2, -1) & (2, -1, 4) respectively. Then the work done by the force is :

Q. A particle is moved from

(0, 0)

(a, a)

under a force

\to F = (3^i + 4^j)

from two paths. Path

1

O P

and path

2

O Q P

. Let

W_{1}

and

W_{2}

be the work done by this force along respective paths. Then

Join BYJU'S Learning Program

A particle moves under the action of a force →F=α^i+2^j along a line y + x = 1. If work done by the force along the path is zero, then α is

The correct option is A 2W=→F.→dr=(α^i+2^j).(dx^i+dy^j)W=αdx+2dy=0αdx=−2dydydx=−α2Giveny+x=1dydx=−1 On comparing, we get −α2 = −1⇒α = 2

A particle moves under the action of a force $\to F = α^i + 2^j$ along a line y + x = 1. If work done by the force along the path is zero, then $α$ is

The correct option is A $2$
$W = \to F . \to d r = (α^i + 2^j) . (d x^i + d y^j) W = α d x + 2 d y = 0 α d x = - 2 d y \frac{d y}{d x} = \frac{- α}{2} G i v e n y + x = 1 \frac{d y}{d x} = - 1$
On comparing, we get
$- \frac{α}{2} = - 1 \Rightarrow α = 2$