Question

Heya mates...

Answer them.♠

1. A body is projected horizontally from top of a building of height h . Velocity of projection is u find?

a) The time it will take to reach the ground.
b) Horizontal distance from foot of a building where it will strike the ground
C) Velocity with which the body reach the ground

2. Derive an expression for maximum speed of a vehicle should have to take a turn on a banked road. Hence deduce an expression for angle of banking at which there is minimum wear and tear to the tyres of the vehicle.

3. Calculate moment of inertia of circular disc( All four cases)?

4. Show that for small oscillations the motion of a simple pendulum is simple harmonic . Derive an expression for its time period. Does it depend on the mass of the bob?

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Answer 1

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Answer 2

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A motion be Simple harmonic motion only when ,

1. Acceleration of particle is just opposite to motion of body

2. Acceleration is directly proportional to displacement e.g., a = -ω²x

A pendulum moves in such a way that angle is formed by it is θ , as you know , along tangent , motion of pendulum is just opposite to force. As shown in figure.

now, restoring force , F = -mgsinθ ,

When displacement of pendulum is very small , then sinθ ≈ θ

so, F = -mgθ, also here it is clear , θ = x/L

∴F = -mgx/L

Now use F = ma { Newton's second law }

ma = -mgx/L ⇒ a = -gx/L

Here what you see both the above conditions are satisfied when displacement of pendulum is small.

Now, comapre both the expressions ,

∴ω² = g/L

we know, ω = 2π/T , here T is time period .

so, {2π/T}² = g/L

⇒ T = 2π√{L/g}

Hence, for pendulum time period is T = 2π√{L/g}