A body of mass 4 kg is placed on a plane at | vedclass

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

Question

(B) Given: Mass $m = 4 \ kg$,Force $\overrightarrow{F} = (2 \hat{i} + 3 \hat{j}) \ N$,Displacement $\overrightarrow{d} = \overrightarrow{OQ} - \overri

Vedclass · Accepted Answer

$6: 13$

Vedclass · Answer

(B) Given: Mass $m = 4 \ kg$,Force $\overrightarrow{F} = (2 \hat{i} + 3 \hat{j}) \ N$,Displacement $\overrightarrow{d} = \overrightarrow{OQ} - \overrightarrow{OP} = (6-3) \hat{i} + (10-4) \hat{j} = (3 \hat{i} + 6 \hat{j}) \ m$,Time $t = 4 \ s$.Work done $W = \overrightarrow{F} \cdot \overrightarrow{d} = (2 \hat{i} + 3 \hat{j}) \cdot (3 \hat{i} + 6 \hat{j}) = (2 	imes 3) + (3 	imes 6) = 6 + 18 = 24 \ J$.Average power $\langle P angle = \frac{W}{t} = \frac{24}{4} = 6 \ W$.Acceleration $\overrightarrow{a} = \frac{\overrightarrow{F}}{m} = \frac{2 \hat{i} + 3 \hat{j}}{4} = (0.5 \hat{i} + 0.75 \hat{j}) \ m/s^2$.Velocity at $t = 4 \ s$ is $\overrightarrow{v} = \overrightarrow{u} + \overrightarrow{a}t = 0 + (0.5 \hat{i} + 0.75 \hat{j}) 	imes 4 = (2 \hat{i} + 3 \hat{j}) \ m/s$.Instantaneous power $P_{ins} = \overrightarrow{F} \cdot \overrightarrow{v} = (2 \hat{i} + 3 \hat{j}) \cdot (2 \hat{i} + 3 \hat{j}) = 4 + 9 = 13 \ W$.The ratio of average power to instantaneous power is $\frac{\langle P angle}{P_{ins}} = \frac{6}{13}$.

Similar Questions

At any instant of time $t$, the displacement of a particle is given by $x = 2t - 1$ ($SI$ units) under the influence of a force of $5 \,N$. The value of instantaneous power is (in $SI$ units):

An athlete of mass $60\, kg$ skips at the rate of $20$ steps per minute through an average height of $25\, cm$. The power developed is ............. $W$.

$A$ machine gun fires $300$ bullets per minute, each with a velocity of $500 \,ms^{-1}$. If the mass of each bullet is $4 \,g$, the power of the machine gun is: (in $\,kW$)

$A$ crane of efficiency $80 \%$ is used to lift $8000 \ kg$ of coal from a mine of depth $108 \ m$. If the time taken by the crane to lift the coal is one hour, then the power of the crane (in $kW$) is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

$A$ particle moves with a velocity $\vec{v} = 5\hat{i} - 3\hat{j} + 6\hat{k} \text{ m/s}$ under the influence of a constant force $\vec{F} = 10\hat{i} + 10\hat{j} + 20\hat{k} \text{ N}$. The instantaneous power will be ............... $\text{J/s}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module