NEET Questions

A body is moving with a constant speed in a circular path. Which of the following statements is true about its kinetic energy?

A solid sphere of radius R and mass M rolls down an inclined plane without slipping, making an angle $heta$ with the horizontal. A solid cylinder of the same mass and radius rolls down the same incline. If the sphere takes time $t_s$ and the cylinder takes time $t_c$ to reach the bottom, then the ratio $t_c/t_s$ is:

A solid cylinder is rolling without slipping down an inclined plane. The ratio of its rotational kinetic energy to its total kinetic energy is:

A particle moves along the x-axis under the influence of a variable force given by $F(x) = \frac{a}{x^2} + bx$, where 'a' and 'b' are positive constants. If the particle starts from rest at $x = x_0$, what is the work done by the force when the particle reaches $x = 2x_0$?

A force $\vec{F} = (3x^2\hat{i} + 4y\hat{j})$ N acts on a particle as it moves from (0,0) to (1,1) m. Which of the following paths requires the least amount of work done by the force?

A particle of mass 'm' moves under the influence of a central force given by $F(r) = -\frac{k}{r^3}$, where 'k' is a positive constant. If the particle's initial velocity is 'v' at a distance 'r' from the center of the force, what is the minimum velocity required for the particle to escape to infinity?

A block of mass 'm' is attached to a spring with a variable spring constant given by $k(x) = kx$, where 'k' is a positive constant and 'x' is the extension of the spring. If the block is pulled a distance 'A' from equilibrium and released, what is the maximum speed of the block?

A particle moves in a force field described by the potential energy function $U(x, y) = \frac{1}{2}k(x^2 + y^2)$. The work done by the force field as the particle moves from (1,0) to (0,1) along a circular path centered at the origin is:

A particle is subjected to a force $F = -kx + \frac{a}{x^3}$, where 'k' and 'a' are positive constants. The equilibrium positions are at:

A spring with spring constant $k$ is compressed by a distance $x$. What is the potential energy stored in the spring?