PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Physics

An object follows a curved path. The following quantities may remain constant during the motion

(a) speed
(b) velocity
(c) acceleration
(d) magnitude of acceleration.

Assume that the earth goes round the sun in a circular orbit with a constant speed of 30 kms

The position vector of a particle in a circular motion about the origin sweeps out equal area in equal time. Its
(a) velocity remains constant
(b) speed remains constant
(c) acceleration remains constant
(d) tangential acceleration remains constant.

A particle is going in a spiral path as shown in figure with constant speed.

A car of mass M is moving on a horizontal circular path of radius r. At an instant its speed is v and is increasing at a rate a. 
(a) The acceleration of the car is towards the centre of the path.
(b) The magnitude of the frictional force on the car is greater than \[\frac{\text{mv}^2}{\text{r}}\]

(c) The friction coefficient between the ground and the car is not less than a/g.
(d) The friction coefficient between the ground and the car is \[\mu = \tan^{- 1} \frac{\text{v}^2}{\text{rg}.}\]

Find the acceleration of the moon with respect to the earth from the following data:

Distance between the earth and the moon = 3.85 × 10⁵ km and the time taken by the moon to complete one revolution around the earth = 27.3 days.

Find the acceleration of a particle placed on the surface of the earth at the equator due to earth's rotation. The diameter of earth = 12800 km and it takes 24 hours for the earth to complete one revolution about its axis.

A particle moves in a circle of radius 1.0 cm at a speed given by v = 2.0 t where v is cm/s and t in seconds.
(a) Find the radial acceleration of the particle at t = 1 s.
(b) Find the tangential acceleration at t = 1 s.
(c) Find the magnitude of the acceleration at t = 1 s.

A scooter weighing 150 kg together with its rider moving at 36 km/hr is to take a turn of a radius 30 m. What horizontal force on the scooter is needed to make the turn possible ?

A stone is fastened to one end of a string and is whirled in a vertical circle of radius R. Find the minimum speed the stone can have at the highest point of the circle.

A ceiling fan has a diameter (of the circle through the outer edges of the three blades) of 120 cm and rpm 1500 at full speed. Consider a particle of mass 1 g sticking at the outer end of a blade. How much force does it experience when the fan runs at full speed? Who exerts this force on the particle? How much force does the particle exert on the blade along its surface?

A mosquito is sitting on an L.P. record disc rotating on a turn table at \[33\frac{1}{3}\] revolutions per minute. The distance of the mosquito from the centre of the turn table is 10 cm. Show that the friction coefficient between the record and the mosquito is greater than π²/81. Take g =10 m/s².

A simple pendulum is suspended from the ceiling of a car taking a turn of radius 10 m at a speed of 36 km/h. Find the angle made by he string of the pendulum with the vertical if this angle does not change during the turn. Take g = 10 m/s².

The bob of a simple pendulum of length 1 m has mass 100 g and a speed of 1.4 m/s at the lowest point in its path. Find the tension in the string at this instant. 

Suppose the amplitude of a simple pendulum having a bob of mass m is θ₀. Find the tension in the string when the bob is at its extreme position. 

A person stands on a spring balance at the equator. By what fraction is the balance reading less than his true weight?

A turn of radius 20 m is banked for the vehicles going at a speed of 36 km/h. If the coefficient of static friction between the road and the tyre is 0.4, what are the possible speeds of a vehicle so that it neither slips down nor skids up?

A motorcycle has to move with a constant speed on an over bridge which is in the form of a circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point.(a) What can its maximum velocity be for which the contact with the road is not broken at the highest point? (b) If the motorcycle goes at speed 1/√2 times the maximum found in part (a), where will it lose the contact with the road? (c) What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge? 

A car goes on a horizontal circular road of radius R, the speed increasing at a constant rate \[\frac{\text{dv}}{\text{dt}} = a\] . The friction coefficient between the road and the tyre is μ. Find the speed at which the car will skid.