The work done in moving an object from the or | vedclass

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

Question

(B) We know that the work done $W$ is given by the dot product of force $\vec{F}$ and displacement $\vec{d}$.Given,force $\vec{F} = 2 \hat{i} - \hat{j

Vedclass · Accepted Answer

$9 	ext{ units}$

Vedclass · Answer

(B) We know that the work done $W$ is given by the dot product of force $\vec{F}$ and displacement $\vec{d}$.Given,force $\vec{F} = 2 \hat{i} - \hat{j} - \hat{k}$.The object moves from the origin $(0, 0, 0)$ to the position vector $\vec{r} = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$,so the displacement $\vec{d} = \vec{r} - 0 = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$.Using the property of dot product $\hat{i} \cdot \hat{i} = \hat{j} \cdot \hat{j} = \hat{k} \cdot \hat{k} = 1$ and $\hat{i} \cdot \hat{j} = \hat{j} \cdot \hat{k} = \hat{k} \cdot \hat{i} = 0$,we calculate:$W = \vec{F} \cdot \vec{d} = (2 \hat{i} - \hat{j} - \hat{k}) \cdot (3 \hat{i} + 2 \hat{j} - 5 \hat{k})$$W = (2 	imes 3) + (-1 	imes 2) + (-1 	imes -5)$$W = 6 - 2 + 5 = 9 	ext{ units}$.

The work done in moving an object from the origin to a point whose position vector is $\vec{r} = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$ by a force $\vec{F} = 2 \hat{i} - \hat{j} - \hat{k}$ is:

Similar Questions

$A$ chain of mass $4 \ kg$ and length $2 \ m$ is hanging such that one-fourth of its length is hanging over the edge of a table. The work done to pull the hanging part onto the table is . . . . . . $J$. (Take $g = 10 \ m/s^2$)

At time $t=0$,a particle starts moving along the $x$-axis. If its kinetic energy increases uniformly with time $t$,the net force acting on it must be proportional to

$A$ body of mass $6 \,kg$ is under a force which causes displacement in it given by $s = \frac{t^2}{4} \,m$, where $t$ is time in seconds. The work done by the force in $2 \,s$ is: (in $\,J$)

$A$ body of mass $m$ accelerates uniformly from rest to a speed $v_0$ in time $t_0$. The work done on the body till any time $t$ is

$A$ force $\vec{F} = (-2\hat{i} + 15\hat{j} + 6\hat{k}) \, N$ acts on an object,causing it to move along the $Y$-axis. If the displacement along the $Y$-axis is $10 \, m$,find the work done by the force in $J$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module