Work Energy Theorem

A satellite of mass $m$, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is

A $3 kg$ object has initial velocity $\left(6\widehat{\mathrm{i}}-2\widehat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}.$ The total work done $\left(\mathrm{in} \mathrm{J}\right)$ on the object if its velocity changes to $(8\widehat{\mathrm{i}}+4\widehat{\mathrm{j}}) \mathrm{m} {\mathrm{s}}^{-1}$ is

A variable force acts on body of mass $1 \mathrm{kg}$ and it changes the velocity of the body from $2 \mathrm{m}/\mathrm{s}$ to $6 \mathrm{m}/\mathrm{s}$. Find the work done (in $\mathrm{joule}$) on the body by the variable force.

What is work-energy theorem?

Work energy theorem is applicable for conservative forces only.

A body of mass $0.5 \mathrm{kg}$ travels in a straight line with velocity $v=x^{1/2}$. What is the work done by the net force during its displacement from $x=0$ to $x=2 \mathrm{m}$?

Three identical solid spheres move down through three inclined planes $A, B and C$ all same dimensions, $A$ is without friction, $B$ is undergoing pure rolling and $C$ is rolling with slipping. Compare the kinetic energies $E_A, E_B and E_C$ at the bottom.

A body of mass $2 \mathrm{kg}$ thrown vertically upward from the ground with a velocity of $8 \mathrm{m} {\mathrm{s}}^{-1}$ reaches a maximum height of $3 \mathrm{m}$. Magnitude of work done by the air resistance is (Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

A car of mass $2000 \mathrm{kg}$ is moving at a speed of $20 {\mathrm{ms}}^{-1}$ up an inclined plane making an angle $30°$ with the horizontal. At some point, the motor stops, and the car continues to move along the plane due to its initial velocity. If it is just able to reach the destination which is at a height of $10 \mathrm{m}$ above the point, calculate the work done against friction acting between the tyres of the car and the plane. (Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

An object of mass $8 \mathrm{kg}$ moves along positive $X-$axis. When it passes through $X=0,$ a constant force directed along the negative $X-$axis begins to act on it. The kinetic energy of the object is found to be $0$ and $30 \mathrm{J}$ for $X=5 \mathrm{m}$ and $X=0 \mathrm{m}$ respectively. If the force continues to act further, then the object moves back along negative $X-$axis. The speed of the object when it reaches $X=-3 \mathrm{m}$

Under the action of a force, a $2 \mathrm{kg}$ body moves such that its position $x$ as a function of time is given by $x=\frac{t^3}{3}$, where $x$ is in metre and $t\mathit{ }$in second. What will be the work done by the force in the first two seconds?

What minimum horizontal velocity has to be imparted the ball suspended from a thread of length $l$ for it to reach the height of the suspension?

What is the critical speed of block of mass $m$tied to one end of a string which is whirled round in a vertical circle of a radius $R$ at the top of the circle?

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because

A body of mass $3 \mathrm{kg}$ is put under a forces which in turn causes a displacement in it is given by $S=\frac{t^3}{3}$ $\left(\mathrm{in} \mathrm{m}\right).$What will be the work done by the force in first $2 \mathrm{s}$ ?

If a solid cylinder of mass $3\mathit{ }\mathrm{kg}$ is rolling on a horizontal surface with a velocity of $4\mathit{ }\mathrm{m} {\mathrm{s}}^{-1}$. It collides with a horizontal spring of spring constant $200\mathit{ }\mathrm{N} {\mathrm{m}}^{-1}$. What will be the maximum compression produced in the spring?

A curved surface is shown in figure. The portion $BCD$is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from $A$ which is at a slightly greater height than $C$.

With the surface $AB$, ball $1$ has large enough friction to cause rolling down without slipping. Ball $2$ has a small friction and ball $3$ has a negligible friction.

For balls which do not reach $D$, which of the balls can reach back $A$?

A small block of mass $m$ is released from point $A$ on a fixed smooth wedge, as shown in the figure. Bottom of the wedge is marked as $B$ and at a point $C$, the block will stop moving because the straight path of the floor is rough.

The velocity of the block at the mid-point between $B$ to $C$ will be

 A small block of mass $m$ is released from point $A$ on a fixed smooth wedge, as shown in the figure. Bottom of the wedge is marked as $B$ and at a point $C$, the block will stop moving because the straight path of the floor is rough.

The friction coefficient of the block with the floor is

If total mechanical energy of the particle is $-40 \mathrm{J}$, then it can be found in region