List of top Physics Questions on work, energy and power

Two masses \(m\) and \(2m\) are connected by a light string going over a pulley (disc) of mass \(30m\) with radius \(r=0.1\,\text{m}\). The pulley is mounted in a vertical plane and is free to rotate about its axis. The \(2m\) mass is released from rest and its speed when it has descended through a height of \(3.6\,\text{m}\) is ____________ m/s. (Assume string does not slip and \(g=10\,\text{m s}^{-2}\)).

Given below are two statements:
Statement I: An object moves from position \( \vec{r}_1 \) to position \( \vec{r}_2 \) under a conservative force field \( \vec{F} \). The work done by the force is \[ W = -\int_{\vec{r}_1}^{\vec{r}_2} \vec{F} \cdot d\vec{r}. \]
Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of the above statements, choose the correct answer from the options given below:

A large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in figure. The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass $M$ as $\mu$, is :

A body of mass 4 kg is placed on a plane at a point P having coordinate $(3,4)$ m. Under the action of force $\vec{F} = (2\hat{i} + 3\hat{j})$ N, it moves to a new point Q having coordinates $(6,10)$ m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of:

Position \( x \) of the particle of mass 2 kg varies as function of time as \( x = t^2 + t + 1 \). Find out work done on the particle from \( t_1 = 2 \) sec to \( t_2 = 3 \) sec.

A ball of mass 100 g is projected with velocity 20 m/s at $60^\circ$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is:

A curve is given between the potential energy \(U\) of a particle and its position on the \(x\)-axis as shown. Given: \[ \tan\theta_1 = 1,\qquad \tan\theta_2 = 3,\qquad \tan\theta_3 = -\frac{1}{2} \] If \(F_{AB}\) is the force acting on the particle during motion from \(A\) to \(B\), similarly \(F_{BC}\), \(F_{CD}\) and \(F_{DE}\) are the forces during \(B\) to \(C\), \(C\) to \(D\) and \(D\) to \(E\) respectively, arrange the magnitudes of these forces in decreasing order.

A curve is given between potential energy of a particle and its position on the x-axis.

Given: \( \tan \theta_1 = 1, \, \tan \theta_2 = 3, \, \tan \theta_3 = -\frac{1}{2} \)
If \( F_{AB} \) be the force acting on the particle during \( A \) to \( B \), similarly \( F_{BC}, F_{CD}, \, F_{DE} \) are the forces during \( B \) to \( C \), \( C \) to \( D \), and \( D \) to \( E \) respectively. Arrange magnitudes of these forces in decreasing order.

A body of mass 2 kg is moving with a velocity of 5 m/s. How much work is required to stop the body?

If a force of $ 10 \, \text{N} $ displaces a body by $ 5 \, \text{m} $ in the direction of the force, the work done is: