NEET Questions

A particle moves along the x-axis under the influence of a force $F(x) = -kx^2$. If the particle moves from $x = a$ to $x = 2a$, the work done by the force is:

A force $\vec{F} = (2x + 3)\hat{i}$ N acts on a particle as it moves from $x = 0$ to $x = 2$ m. The work done by the force is:

A body covers one-third of its journey with speed 'u', the next one-third with speed 'v', and the last one-third with speed 'w'. What is its average speed for the entire journey?

A car travels from point A to point B with a speed of 40 km/h and returns from B to A with a speed of 60 km/h. What is its average speed for the entire journey?

A solid sphere rolls without slipping down an inclined plane of angle $heta$. What fraction of its total kinetic energy is rotational?

A spring of force constant 'k' is compressed by a distance 'x' and used to launch a block of mass 'm' up a frictionless incline of angle $heta$. What is the maximum distance 'd' the block travels along the incline before momentarily coming to rest?

A particle is projected with kinetic energy $K$ at an angle of $60^\circ$ with the horizontal. The kinetic energy of the particle at the highest point of its trajectory will be:

A block of mass $m$ is released from rest at a height $h$ on a smooth inclined plane of inclination $heta$. The kinetic energy of the block at the bottom of the incline is:

A particle moves in one dimension under the influence of a conservative force with potential energy $U(x) = ax^3 - bx$, where $a$ and $b$ are positive constants. The equilibrium position of the particle is at:

A swimmer can swim with a speed of 4 m/s in still water. He wants to cross a river of width 200 m, flowing with a speed of 2 m/s. If he wants to reach directly opposite to the starting point, at what angle with the downstream direction should he swim?