NEET Questions

A block of mass $m$ is placed on a rough inclined plane with an angle of inclination $heta$. The coefficient of static friction between the block and the plane is $\mu_s$. A horizontal force $F$ is applied to the block. For what range of values of $F$ will the block remain at rest?

Two blocks of masses $m_1$ and $m_2$ are connected by a massless string passing over a smooth pulley. The coefficient of kinetic friction between $m_1$ and the horizontal surface is $\mu_k$. If $m_2$ is descending with a constant acceleration $a$, what is the tension in the string?

A block is projected up a rough inclined plane with an initial velocity $u$. The coefficient of kinetic friction between the block and the plane is $\mu_k$. The block travels a distance $s$ up the plane before coming to rest. What is the angle of inclination $heta$ of the plane?

A block of mass $m$ rests on a horizontal surface with coefficient of static friction $\mu_s$. A force $F$ is applied at an angle $heta$ to the horizontal. The minimum force required to just move the block is:

A car is moving with uniform speed on a banked road inclined at an angle $heta$. The coefficient of static friction between the tyres and road is $\mu_s$. What is the maximum speed with which the car can negotiate the curve without skidding, if the radius of the curve is $R$?

A block of mass $m$ is placed on a rough rotating disc at a distance $r$ from the center. The coefficient of static friction is $\mu_s$. What is the maximum angular speed $\omega$ for which the block will not slip?

A particle moves in a plane with a velocity given by $\vec{v} = (A\omega cos(\omega t))\hat{i} + (B\omega sin(\omega t))\hat{j}$. If the particle starts from the origin at $t=0$, the equation of the trajectory is:

A rod of length $L$ is hinged at one end and is free to rotate in a vertical plane. It is released from rest in the horizontal position. The angular acceleration of the rod when it makes an angle $heta$ with the vertical is:

A particle of mass $m$ moves under the influence of a central force given by $F(r) = -k/r^3$. If the particle's orbit is circular with radius $r_0$, its time period of revolution is:

A thin uniform disc of mass $M$ and radius $R$ is rotating with angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. A thin ring of mass $m$ and radius $r$ is gently placed on the disc concentrically. The final angular velocity of the combined system is: