Science (English Medium) इयत्ता ११ - CBSE Question Bank Solutions for Physics

Two particles of masses m₁ and m₂ are joined by a light rigid rod of length r. The system rotates at an angular speed ω about an axis through the centre of mass of the system and perpendicular to the rod. Show that the angular momentum of the system is \[L = \mu r^2 \omega\] where \[\mu\] is the reduced mass of the system defined as \[\mu = \frac{m_1 + m_2}{m_1 + m_2}\]

Suppose the platform with the kid in the previous problem is rotating in anticlockwise direction at an angular speed ω. The kid starts walking along the rim with a speed \[\nu\] relative to the platform also in the anticlockwise direction. Find the new angular speed of the platform.

A uniform rod of mass m and length l is struck at an end by a force F perpendicular to the rod for a short time interval t. Calculate (a) the speed of the centre of mass, (b) the angular speed of the rod about the centre of mass, (c) the kinetic energy of the rod and (d) the angular momentum of the rod about the centre of mass after the force has stopped to act. Assume that t is so small that the rod does not appreciably change its direction while the force acts.

Two small balls A and B, each of mass m, are joined rigidly by a light horizontal rod of length L. The rod is clamped at the centre in such a way that it can rotate freely about a vertical axis through its centre. The system is rotated with an angular speed ω about the axis. A particle P of mass m kept at rest sticks to the ball A as the ball collides with it. Find the new angular speed of the rod.

Suppose the rod with the balls A and B of the previous problem is clamped at the centre in such a way that it can rotate freely about a horizontal axis through the clamp. The system is kept at rest in the horizontal position. A particle P of the same mass m is dropped from a height h on the ball B. The particle collides with B and sticks to it. (a) Find the angular momentum and the angular speed of the system just after the collision. (b) What should be the minimum value of h so that the system makes a full rotation after the collision.

A uniform wheel of radius R is set into rotation about its axis at an angular speed ω. This rotating wheel is now placed on a rough horizontal surface with its axis horizontal. Because of friction at the contact, the wheel accelerates forward and its rotation decelerates till the wheel starts pure rolling on the surface. Find the linear speed of the wheel after it starts pure rolling.

A thin spherical shell lying on a rough horizontal surface is hits by a cue in such a way that the line of action passes through the centre of the shell. As a result, the shell starts moving with a linear speed \[\nu\] without any initial angular velocity. Find the linear speed of the shell after it starts pure rolling on the surface.

A solid sphere is set into motion on a rough horizontal surface with a linear speed ν in the forward direction and an angular speed ν/R in the anticlockwise directions as shown in the following figure. Find the linear speed of the sphere (a) when it stops rotating and (b) when slipping finally ceases and pure rolling starts.

A solid sphere rolling on a rough horizontal surface with a linear speed ν collides elastically with a fixed, smooth, vertical wall. Find the speed of the sphere after it has started pure rolling in the backward direction.

At a metro station, a girl walks up a stationary escalator in time t₁. If she remains stationary on the escalator, then the escalator take her up in time t₂. The time taken by her to walk up on the moving escalator will be ______.

For the one-dimensional motion, described by x = t – sint

1. x (t) > 0 for all t > 0.
2. v (t) > 0 for all t > 0.
3. a (t) > 0 for all t > 0.
4. v (t) lies between 0 and 2.

A spring with one end attached to a mass and the other to a rigid support is stretched and released.

1. Magnitude of acceleration, when just released is maximum.
2. Magnitude of acceleration, when at equilibrium position, is maximum.
3. Speed is maximum when mass is at equilibrium position.
4. Magnitude of displacement is always maximum whenever speed is minimum.

A ball is bouncing elastically with a speed 1 m/s between walls of a railway compartment of size 10 m in a direction perpendicular to walls. The train is moving at a constant velocity of 10 m/s parallel to the direction of motion of the ball. As seen from the ground ______.

1. the direction of motion of the ball changes every 10 seconds.
2. speed of ball changes every 10 seconds.
3. average speed of ball over any 20 second interval is fixed.
4. the acceleration of ball is the same as from the train.

Give examples of a one-dimensional motion where

1. the particle moving along positive x-direction comes to rest periodically and moves forward.
2. the particle moving along positive x-direction comes to rest periodically and moves backward.

A motor car moving at a speed of 72 km/h can not come to a stop in less than 3.0 s while for a truck this time interval is 5.0 s. On a highway the car is behind the truck both moving at 72 km/h. The truck gives a signal that it is going to stop at emergency. At what distance the car should be from the truck so that it does not bump into (collide with) the truck. Human response time is 0.5 s.

A particle falling vertically from a height hits a plane surface inclined to horizontal at an angle θ with speed vo and rebounds elastically (Figure). Find the distance along the plane where if will hit second time.

A man wants to reach from A to the opposite corner of the square C (Figure). The sides of the square are 100 m. A central square of 50 m × 50 m is filled with sand. Outside this square, he can walk at a speed 1 m/s. In the central square, he can walk only at a speed of v m/s (v < 1). What is smallest value of v for which he can reach faster via a straight path through the sand than any path in the square outside the sand?

A ball is travelling with uniform translatory motion. This means that ______.

Why are porcelain objects wrapped in paper or straw before packing for transportation?

The displacement vector of a particle of mass m is given by `r(t) = hati` A cos ωt + `hatj` B sin ωt. Show that the trajectory is an ellipse.