A particle moves along the x-axis under the influence of a conservative force given by $F(x) = -kx^3$. If the particle is released from rest at $x = A$, what is its speed when it reaches $x = A/2$?

Water is drawn from a well in a 5 kg drum of capacity 55 L by two ropes connected to the top of the drum. The linear mass density of each rope is $0.5{\rm{\;kg}}{{\rm{m}}^{ - 1}}$. The work done in lifting water to the ground from the surface of water in the well 20 m below is $\left[ {{\rm{g}} = 10{\rm{m}}{{\rm{s}}^{ - 2}}} \right]$

In which case does the potential energy decrease

The potential energy of a system increases if work is done

The decrease in the potential energy of a ball of mass 20 kg which falls from a height of 50 cm is

A particle moves along the x-axis under the influence of a conservative force given by $F(x) = -kx^3$. If the particle is released from rest at $x = A$, what is its speed when it reaches $x = A/2$?

A mass of 50 kg is raised through a certain height by a machine whose efficiency is $90\%$, the energy is 5000 J. If the mass is now released, its KE on hitting the ground shall be

A particle is projected vertically upwards with a speed $u$ from the surface of the Earth. If the air resistance is proportional to the square of the velocity ($F = -kv^2$), what is the maximum height reached by the particle? (Assume $g$ is constant and $m$ is the mass of the particle)

A block of mass 2 kg is lifted vertically through a height of 3 m. The change in its potential energy is (g = 10 m/s²):

A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?

The decrease in the potential energy of a ball of mass 20 kg which falls from a height of 50 cm is