Embibe Experts Solutions for Chapter: Work, Energy and Power, Exercise 7: Exercise (Analytical Questions)

‘A body of mass $10 \text{Kg}$ is displaced from point $A\left(2,1,3\right)$ to point B(3, 3, 4) $B\left(3,3,4\right)$under the effect of a force of magnitude $20 \text{N}$ in the direction of $6\hat{i} + 8\hat{j}.$ Calculate W.D. by the force :

A body of mass $m$, accelerates uniformly from rest to $v_1$ in time $t_1$. The instantaneous power delivered to the body as a function of time $t$ is

The only force F_x acting on a 2.0 kg body, as it moves along the x-axis varies as shown in the figure. The velocity of the body along positive x-axis at x = 0 is 4 m/s. The kinetic energy of the body at x = 3 m is : 

A machine which is $75\%$ efficient, uses $12 \mathrm{J}$ of energy in lifting $1 \mathrm{kg}$ mass through a certain distance. The mass is then allowed to fall through the same distance, the velocity at the end of its fall is :-

A variable force, given by the 2-dimensional vector $\overrightarrow{F}=(3{\mathrm{x}}^2\hat{\mathrm{i}} + 4\hat{\mathrm{j}})$, acts on a particle. The force is in newton and $x$ is in metre. What is the change in the kinetic energy of the particle as it moves from the point with coordinates $(2, 3)$ to $(3, 0)$ ? (The coordinates are in meters)

A mass $m$ is attached to the end of a rod of length $l$. The mass goes along a vertical circular path with the other end hinged at its centre. What should be the minimum velocity of the mass at the bottom of the circle so that the mass completes the circle?

A stone is tied to a string of length $l$ and is whirled in a vertical circle with the other end of the string as the centre.At a certain instant of time, the stone is at its lowest position and has a speed $u$.The magnitude of the change in velocity as it reaches a position where the string is horizontal ($g$ being acceleration due to gravity)