A body of mass 2 ,kg moving in X-Y plane has | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The force acting on the body is given by $\vec{F} = -
abla U = -(\frac{\partial U}{\partial x} \hat{i} + \frac{\partial U}{\partial y} \hat{j}) =

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(A) The force acting on the body is given by $\vec{F} = -
abla U = -(\frac{\partial U}{\partial x} \hat{i} + \frac{\partial U}{\partial y} \hat{j}) = -(6 \hat{i} + 8 \hat{j}) \,N$.The acceleration of the body is $\vec{a} = \frac{\vec{F}}{m} = \frac{-(6 \hat{i} + 8 \hat{j})}{2} = -(3 \hat{i} + 4 \hat{j}) \,m/s^2$.Since the body starts from rest at $t = 0$, its velocity at $t = 2 \,s$ is $\vec{v} = \vec{u} + \vec{a}t = 0 + (-(3 \hat{i} + 4 \hat{j})) 	imes 2 = -(6 \hat{i} + 8 \hat{j}) \,m/s$.The kinetic energy of the body at $t = 2 \,s$ is $K = \frac{1}{2} m v^2 = \frac{1}{2} 	imes 2 	imes ((-6)^2 + (-8)^2) = 36 + 64 = 100 \,J$.According to the work-energy theorem, the work done by the external force is equal to the change in kinetic energy. Since the body starts from rest $(K_i = 0)$, the work done by the force is $W = \Delta K = 100 - 0 = 100 \,J$.

$A$ body of mass $2 \,kg$ moving in $X-Y$ plane has a potential energy given by $U = (6x + 8y) \,J$. The body is at rest at the point $(3, 2) \,m$. The work done by the body to reach another position after $2 \,s$ is: (in $\,J$)

Similar Questions

$A$ small block of mass $m$ slides along a smooth track as shown in the figure. If it starts from rest at point $P$,what is the velocity of the block at point $Q$?

$A$ sphere is suspended by a thread of length $\ell$. What minimum horizontal velocity has to be imparted to the sphere for it to reach the height of the suspension point?

$A$ car moving with a velocity of $10 \, m/s$ can be stopped by the application of a constant force $F$ in a distance of $20 \, m$. If the velocity of the car is $30 \, m/s$,it can be stopped by this same force in what distance (in $, m$)?

$A$ particle is released from a height $s$. At a certain height,its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively:

$A$ uniform flexible chain of mass $m$ and length $2l$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of the chain when it leaves the pin is

Vedclass Test Series

Exam Paper Generator

Online Exam Module