Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is \[\frac{1}{2}k x^2\] . The possible cases are

(a) at spring was initially compressed by a distance x and was finally in its natural length
(b) it was initially stretched by a distance x and and finally was in its natural length
(c) it was initially in its natural length and finally in a compressed position
(d) it was initially in its natural length and finally in a stretched position.

If the sum of all the forces acting on a body is zero, is it necessarily in equilibrium? If the sum of all the forces on a particle is zero, is it necessarily in equilibrium?

Following figure shows a spring fixed at the bottom end of an incline of inclination 37°. A small block  of mass 2 kg starts slipping down the incline from a point 4⋅8 m away from the spring. The block compresses the spring by 20 cm, stops momentarily and then rebounds through a distance of 1 m up the incline. Find (a) the friction coefficient between the plane and the block and (b) the spring constant of the spring. Take g = 10 m/s².

A block of mass m moving at a speed ν compresses a spring through a distance x before its speed is halved. Find the spring constant of the spring.

Consider the situation shown in the following figure. Initially the spring is unstretched when the system is released from rest. Assuming no friction in the pulley, find the maximum elongation of the spring.

A block of mass m sliding on a smooth horizontal surface with a velocity \[\vec{\nu}\] meets a long horizontal spring fixed at one end and with spring constant k, as shown in following figure following. Find the maximum compression of the spring. Will the velocity of the block be the same as  \[\vec{\nu}\]  when it comes back to the original position shown?

A small block of mass 100 g is pressed against a horizontal spring fixed at one end to compress the spring through 5 cm (figure following). The spring constant is 100 N/m. When released, the block moves horizontally till it leaves the spring. Where will it hit the ground 2 m below the spring?

A uniform ladder of length 10⋅0 m and mass 16⋅0 kg is resting against a vertical wall making an angle of 37° with it. The vertical wall is frictionless but the ground is rough. An electrician weighing 60⋅0 kg climbs up the ladder. If he stays on the ladder at a point 8⋅00 m from the lower end, what will be the normal force and the force of friction on the ladder by the ground? What should be the minimum coefficient of friction for the electrician to work safely?

Suppose the friction coefficient between the ground and
the ladder of the previous problem is 0.540. Find the
maximum weight of a mechanic who could go up and do
the work from the same position of the ladder.

The door of an almirah is 6 ft high, 1⋅5 ft wide and weighs 8 kg. The door is supported by two hinges situated at a distance of 1 ft from the ends. If the magnitudes of the forces exerted by the hinges on the door are equal, find this magnitude.

The force of viscosity is

The viscous force acting between two layers of a liquid is given by \[\frac{F}{A} = - \eta\frac{dv}{dz}\]. This F/A may be called 

A raindrop falls near the surface of the earth with almost uniform velocity because

A spherical ball is dropped in a long column of a viscous liquid. The speed of the ball as a function of time may be best represented by the graph 

In discussing Doppler effect, we use the word "apparent frequency". Does it mean that the frequency of the sound is still that of the source and it is some physiological phenomenon in the listener's ear that gives rise to Doppler effect? Think for the observer approaching the source and for the source approaching the observer.

The engine of a train sounds a whistle at frequency v. The frequency heard by a passenger is

The change in frequency due to Doppler effect does not depend on

A metal sphere of radius 1 mm and mass 50 mg falls vertically in glycerine. Find (a) the viscous force exerted by the glycerine on the sphere when the speed of the sphere is 1 cm s⁻¹, (b) the hydrostatic force exerted by the glycerine on the sphere and (c) the terminal velocity with which the sphere will move down without acceleration. Density of glycerine = 1260 kg m⁻³ and its coefficient of viscosity at room temperature = 8.0 poise.