Science (English Medium) Class 11 - CBSE Question Bank Solutions for Physics

A particle is projected with a speed u at an angle θ with the horizontal. Consider a small part of its path near the highest position and take it approximately to be a circular arc. What is the radius of this circular circle? This radius is called the radius of curvature of the curve at the point.

What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle θ/2 with the horizontal?

A block of mass m moves on a horizontal circle against the wall of a cylindrical room of radius R. The floor of the room on which the block moves is smooth but the friction coefficient between the wall and the block is μ. The block is given an initial speed v₀. As a function of the speed v writes
(a) the normal force by the wall on the block,
(b) the frictional force by a wall, and
(c) the tangential acceleration of the block.
(d) Integrate the tangential acceleration \[\left( \frac{dv}{dt} = v\frac{dv}{ds} \right)\] to obtain the speed of the block after one revolution.

A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular  velocity ω in a circular path of radius R (In the following figure). A smooth groove AB of length L(<<R) is made the surface of the table. The groove makes an angle θ with the radius OA of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released to move at the point A in the groove and is released to move along AB. Find the time taken by the particle to reach the point B.

A car moving at a speed of 36 km/hr is taking a turn on a circular road of radius 50 m. A small wooden plate is kept on the seat with its plane perpendicular to the radius of the circular road (In the following figure). A small block of mass 100 g is kept on the seat which rests against the plate. the friction coefficient between the block and the plate is. (a) Find the normal contact force exerted by the plate on the block. (b) The plate is slowly turned so that the angle between the normal to the plate and the radius of the road slowly increases. Find the angle at which the block will just start sliding on the plate.

A table with smooth horizontal surface is placed in a circle of a large radius R (In the following figure). A smooth pulley of small radius is fastened to the table. Two masses m and 2m placed on the table are connected through a string going over the pulley. Initially the masses are held by a person with the string along the outward radius and then the  system is released from rest (with respect to the cabin). Find the magnitude of the initial acceleration of the masses as seen from the cabin and the tension in the string.

A nut becomes loose and gets detached from a satellite revolving around the earth. Will it land on the earth? If yes, where will it land? If no, how can an astronaut make it land on the earth?

Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?

Consider earth satellites in circular orbits. A geostationary satellite must be at a height of about 36000 km from the earth's surface. Will any satellite moving at this height be a geostationary satellite? Will any satellite moving at this height have a time period of 24 hours?

No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?

As the earth rotates about its axis, a person living in his house at the equator goes in a circular orbit of radius equal to the radius of the earth. Why does he/she not feel weightless as a satellite passenger does?

Two satellites going in equatorial plane have almost same radii. As seen from the earth one moves from east one to west and the other from west to east. Will they have the same time period as seen from the earth? If not which one will have less time period?

A spacecraft consumes more fuel in going from the earth to the moon than it takes for a return trip. Comment on this statement.

The time period of an earth-satellite in circular orbit is independent of

A satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the earth. The escape speed from the earth is v_e. Its speed with respect to the satellite

Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.

A body stretches a spring by a particular length at the earth's surface at the equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.

At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the day in this situation?

A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T₀. (a) Find the speed of the ship due to rotation of the earth about its axis. (b) Find the difference between T₀ and the earth's attraction on the bob. (c) If the ship sails at speed v, what is the tension in the string? Angular speed of earth's rotation is ω and radius of the earth is R.