NEET Questions

A wire with mass per unit length $1.0 \, kg \, m^{-1}$ rests on a frictionless inclined plane at $30^\circ$ to the horizontal. A uniform magnetic field of $0.1 \, T$ is applied perpendicular to the plane. What steady current in the wire will prevent it from sliding down the incline?

A metallic rod of linear mass density $2 \, kg/m$ lies on a smooth inclined plane tilted at $60^\circ$ to the horizontal. A uniform magnetic field of $0.4 \, T$ is applied vertically upwards. What current should flow through the rod to keep it stationary?

A conducting rod of mass per unit length $0.8 \, kg/m$ is resting on a frictionless inclined plane making an angle of $30^\circ$ with the horizontal. A uniform magnetic field of $0.2 \, T$ acts vertically upwards. Determine the magnitude and direction of the current in the rod to prevent it from sliding down the incline.

A solid disk and a solid sphere have the same radius but different masses. They are released simultaneously from rest at the top of identical inclined planes. Which object reaches the bottom first?

A ring and a disk, both with equal masses and radii, are released simultaneously from the top of an inclined plane. If the inclined plane is frictionless, which object reaches the bottom first?

A ball is launched with the same initial speed up two smooth inclined planes. The first plane is at an angle of $30^o$ and the ball travels a distance $d_1$. The second plane is at an angle of $60^o$ and the ball travels a distance $d_2$. If the launch angle with the horizontal is the same in both cases, what is the ratio $d_1:d_2$?

A projectile is launched with velocity $v$ at an angle $heta$ with the horizontal up a smooth inclined plane of angle $45^o$. It travels a distance $x$. If the plane's angle is changed to $30^o$, keeping the launch velocity and angle constant, the projectile travels a distance $y$. Find the ratio $x:y$.

Two identical projectiles are launched with the same initial speed. Projectile A is launched up a smooth incline of $30^o$ and travels a distance $L_A$. Projectile B is launched up a smooth incline of $60^o$ and travels a distance $L_B$. If the launch angles with respect to the horizontal are the same for both projectiles, which of the following is true?

A small block is projected up a frictionless inclined plane with an initial speed 'u'. The plane is inclined at an angle 'α' with the horizontal. The block travels a distance 'd' along the plane before coming to rest. If the angle of inclination is doubled to '2α', while keeping the initial speed 'u' constant, will the distance traveled by the block along the plane increase, decrease, or stay the same? Assume the launch angle with respect to the horizontal remains constant.

A block is placed on a ramp inclined at an angle $heta$ to the horizontal. The coefficient of static friction between the block and the ramp is $\mu_s$. What is the maximum value of $heta$ for which the block will remain stationary? (Take $g = 10 ext{ m/s}^2$)