A particle of mass 5kg moving in the x-y plane has its potential energy given by U=(.-7x+24y.)Joule , x and y being in meter . Initially at t=0 ,the particle is located at the origin (.0,0.) and moving with a velocity of 6[2.4 hati + 0.7 hatj]m/s . Find the magnitude of force acting on the particle.

Question

A particle of mass 5kg moving in the x-y plane has its potential energy given by U=(.-7x+24y.)Joule , x and y being in meter . Initially at t=0 ,the particle is located at the origin (.0,0.) and moving with a velocity of 6[2.4 hati + 0.7 hatj]m/s . Find the magnitude of force acting on the particle. (A) 25units (B) 24units (C) 7units (D) None of these

Tardigrade Admin · Accepted Answer

overset arrow F= -( partial U/ partial x) hati-( partial U/ partial y) hatj=7 hati-24 hatj ∴ | overset arrow F|= √(7)2 + (- 24)2=25 unit

$25 u ni t s$

$24 u ni t s$

$7 u ni t s$

None of these

$F \to = - \frac{\partial U}{\partial x} \hat{i} - \frac{\partial U}{\partial y} \hat{j} = 7 \hat{i} - 24 \hat{j}$
$∴$ $∣ ∣ F \to ∣ ∣ = (7)^{2} + (- 24)^{2} = 25 u ni t$

Q. A particle of mass 5kg moving in the x−y plane has its potential energy given by U=(−7x+24y)Joule , x and y being in meter . Initially at t=0 ,the particle is located at the origin (0,0) and moving with a velocity of 6[2.4i^+0.7j^​]m/s . Find the magnitude of force acting on the particle.

25units

24units

7units

None of these

F→=−∂x∂U​i^−∂y∂U​j^​=7i^−24j^​ ∴ ∣∣​F→∣∣​=(7)2+(−24)2​=25unit

$25 u ni t s$

$24 u ni t s$

$7 u ni t s$

$F \to = - \frac{\partial U}{\partial x} \hat{i} - \frac{\partial U}{\partial y} \hat{j} = 7 \hat{i} - 24 \hat{j}$
$∴$ $∣ ∣ F \to ∣ ∣ = (7)^{2} + (- 24)^{2} = 25 u ni t$