HSC Science Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Physics

Consider the Earth as a homogeneous sphere of radius R and a straight hole is bored in it through its centre. Show that a particle dropped into the hole will execute a simple harmonic motion such that its time period is

T = `2π sqrt("R"/"g")`

Consider a simple pendulum of length l = 0.9 m which is properly placed on a trolley rolling down on a inclined plane which is at θ = 45° with the horizontal. Assuming that the inclined plane is frictionless, calculate the time period of oscillation of the simple pendulum.

Consider two simple harmonic motion along the x and y-axis having the same frequencies but different amplitudes as x = A sin (ωt + φ) (along x-axis) and y = B sin ωt (along y-axis). Then show that

`"x"^2/"A"^2 + "y"^2/"B"^2 - (2"xy")/"AB" cos φ = sin^2 φ`

and also discuss the special cases when

1. φ = 0
2. φ = π
3. φ = `π/2`
4. φ = `π/2` and A = B
5. φ = `π/4`

Note: when a particle is subjected to two simple harmonic motions at right angle to each other the particle may move along different paths. Such paths are called Lissajous figures.

Derive an expression for the pressure exerted by a gas on the basis of the kinetic theory of gases.

Define power.

In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 s. If the speed of sound in water is 1460 ms^-1. What is the distance of an enemy submarine? 

Jupiter is at a distance of 824.7 million km from the Earth. Its angular diameter is measured to be 35.72˝. Calculate the diameter of Jupiter.

If π = 3.14, then the value of π² is ______

Two objects of masses m₁ and m₂ fall from the heights h₁ and h₂ respectively. The ratio of the magnitude of their momenta when they hit the ground is ______

Define a vector. Give examples?

Write a short note on the vector product between two vectors.

Explain in detail the triangle law of addition.

Discuss the properties of scalar and vector products.

Convert the vector `vecr = 3hati + 2hatj` into a unit vector.

What are the resultants of the vector product of two given vectors given by `vecA = 4hati - 2hatj + hatk` and `vecB = 5hati + 3hatj - 4hatk`?

Calculate the area of the triangle for which two of its sides are given by the vectors `vecA = 5hati - 3hatj, vecB = 4hati + 6hatj`

The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B. Then the angle between A and B is ______.

An object of mass m held against a vertical wall by applying horizontal force F as shown in the figure. The minimum value of the force F is ______

Two blocks of masses m and 2m are placed on a smooth horizontal surface as shown. In the first case, only a force F₁ is applied from the left. Later only a force F₂ is applied from the right. If the force acting at the interface of the two blocks in the two cases is the same, then F₁ : F₂ is ______

When an object is at rest on the inclined rough surface, ______