ANNUAL EXAM PAPER 2019 CLASS 11 PHYSICS Section D (SOLUTION FULLY EXPLAINED)

Class XI
Annual Exam - 2018-19
(solved Paper)

Section 'D'

25.  (a) Define angle of friction and angle of repose. Show that both are numerically equal.

    (b) Determine the maximum acceleration of the train in which a box lying on the floor remains stationery given that the coefficient of static friction between the box and the floor of the train is 0.15 taking g= 9.8 ms^-2. 

Solution: (a)

i) Angle of friction
The angle between the resultant force and the normal reaction N in the direction of normal reaction. This angle is denoted by θ.

ii) Angle of Repose

It is defined as the minimum angle of inclination of a plane with the horizontal, such that a body placed on the plane just begins to slide down the incline. It is denoted by α.

OR

a) A body tied to one end of a string is made to revolve in a vertical circle. Derive an expression for the velocity of the body and tension in the string at any point.

b) Hence find:

     i) Tension at the bottom and the top of circle.

    ii) Minimum velocity at the lowest point so that it is just able to complete the loop.

Solution: (a)
Consider a particle of mass m is attached to an in-extensible light string of length r. The particle is moving in a vertical circle of radius r about a fixed-point O.

b)

26. (a) Define Viscosity and write SI unit of coefficient of viscosity.

      (b) A plane is in level flight at constant speed and each of its two wings has an area of 25m². If the speed of air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane's mass (take air density to be 1 kg/m³). 

Solution: (a)

When the fluid is in motion it moves in the form of layers having relative motion. The tendency of a fluid to oppose this relative motion of its layers is called viscosity. Generally, it is the force of friction between different layers of fluid when it is in motion. It is also known as viscous force.

SI unit of viscosity is Poiseuille (poise)

                             1 Poise = 0.1 Ns/m² = 0.1Pa-s

b) 

OR

     (a)  Derive an expression for the excess pressure inside a liquid drop.

     (b)  Explain why to keep a piece of paper horizontal, you should blow over, not under it.

Solution: (a)

(b) when air is blown over a piece of paper, the velocity of air air above the paper increases. so according to Bernoulli's principle, the pressure of air decreases above the paper, this causes a pressure difference of air between the upper and lower part of the paper and this pressure difference gives rise to a lifting force which keeps the paper horizontal.