PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Physics

A wave is described by the equation \[y = \left( 1 \cdot 0  mm \right)  \sin  \pi\left( \frac{x}{2 \cdot 0  cm} - \frac{t}{0 \cdot 01  s} \right) .\] 
(a) Find the time period and the wavelength? (b) Write the equation for the velocity of the particles. Find the speed of the particle at x = 1⋅0 cm at time t = 0⋅01 s. (c) What are the speeds of the particles at x = 3⋅0 cm, 5⋅0 cm and 7⋅0 cm at t = 0⋅01 s?
(d) What are the speeds of the particles at x = 1⋅0 cm at t = 0⋅011, 0⋅012, and 0⋅013 s?

A string of linear mass density 0⋅5 g cm⁻¹ and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at the other end (See figure). The ring can move on a vertical rod. A wave pulse is produced on the string which moves towards the ring at a speed of 20 cm s⁻¹. The pulse is symmetric about its maximum which is located at a distance of 20 cm from the end joined to the ring. (a) Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to region its shape. (b) The shape of the string changes periodically with time. Find this time period. (c) What is the tension in the string?

The speed of sound in a medium depends on

At a prayer meeting, the disciples sing JAI-RAM JAI-RAM. The sound amplified by a loudspeaker comes back after reflection from a building at a distance of 80 m from the meeting. What maximum time interval can be kept between one JAI-RAM and the next JAI-RAM so that the echo does not disturb a listener sitting in the meeting. Speed of sound in air is 320 m s⁻¹.

Find the excess pressure inside (a) a drop of mercury of radius 2 mm (b) a soap bubble of radius 4 mm and (c) an air bubble of radius 4 mm formed inside a tank of water. Surface tension of mercury, soap solution and water are 0.465 N m⁻¹, 0.03 N m⁻¹ and 0.076 N m⁻¹ respectively.

Consider a small surface area of 1 mm² at the top of a mercury drop of radius 4.0 mm. Find the force exerted on this area (a) by the air above it (b) by the mercury below it and (c) by the mercury surface in contact with it. Atmospheric pressure = 1.0 × 10⁵ Pa and surface tension of mercury = 0.465 N m⁻¹.  Neglect the effect of gravity. Assume all numbers to be exact.

The capillaries shown in figure have inner radii 0.5 mm, 1.0 mm and 1.5 mm respectively. The liquid in the beaker is water. Find the heights of water level in the capillaries. The surface tension of water is 7.5 × 10⁻² N m⁻¹. 

Calculate the speed of sound in oxygen from the following data. The mass of 22.4 litre of oxygen at STP (T = 273 K and p = 1.0 × 10⁵ N m⁻²) is 32 g, the molar heat capacity of oxygen at constant volume is C_v = 2.5 R and that at constant pressure is C_p = 3.5 R.

The speed of sound as measured by a student in the laboratory on a winter day is 340 m s⁻¹ when the room temperature is C17°. What speed will be measured by another student repeating the experiment on a day when the room temperature is 32°C?

A barometer is constructed with its tube having radius 1.0 mm. Assume that the surface of mercury in the tube is spherical in shape. If the atmospheric pressure is equal to 76 cm of mercury, what will be the height raised in the barometer tube? The contact angle of mercury with glass = 135° and surface tension of mercury = 0.465 N m⁻¹. Density of mercury = 13600 kg m⁻³. 

A piano wire weighing 6⋅00 g and having a length of 90⋅0 cm emits a fundamental frequency corresponding to the "Middle C" \[\left( \nu = 261 \cdot 63  Hz \right)\]. Find the tension in the wire.

Find the change in the volume of 1.0 litre kerosene when it is subjected to an extra pressure of 2.0 × 10⁵ N m⁻² from the following data. Density of kerosene = 800 kg m⁻³and speed of sound in kerosene = 1330 ms⁻¹.

A capillary tube of radius 1 mm is kept vertical with the lower end in water. (a) Find the height of water raised in the capillary. (b) If the length of the capillary tube is half the answer of part , find the angle θ made by the water surface in the capillary with the wall.

A one-metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops?

The lower end of a capillary tube of radius 1 mm is dipped vertically into mercury. (a) Find the depression of mercury column in the capillary. (b) If the length dipped inside is half the answer of part (a), find the angle made by the mercury surface at the end of the capillary with the vertical. Surface tension of mercury = 0.465 N m⁻¹ and the contact angle of mercury with glass −135 °.