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3 years ago

Check the correctness of formula t=2π √m/k, dimensionally

Physics

1 answer:

pantera1 [17]3 years ago

4 0

Hi there! Lets see!

m is mass, and its units are kg
k is the elastic constant measured in newtons per meter (N/m), or kilograms per second squared kg/s²

Therefore:

$\sqrt{\dfrac{m}{k}} =\sqrt{\dfrac{[kg]}{[\dfrac{kg}{s^2}]}} =\sqrt{\dfrac{[kg]}{[kg]}\cdot s^2} = \sqrt{[s]^2} = s$

The period is given in seconds so the formula is dimensionally correct.

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4 years ago

Different velocity-time graph lines are shown, displaying the behavior of multiple race carts along a linear track.

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3 years ago

Read 2 more answers

If the particles are oxygen ions carrying a charge of −2e and the magnetic field magnitude is 0.12 T , how long does it take eac

Natali5045456 [20]

Time taken by each ion to travel the semicircular path through the magnetic field is 34 X 10⁻²⁶s.

<u>Explanation:</u>

Given:

Charge of oxygen ion, q = -2

Magnetic Field, B = 0.12 T

Mass of O₂ , m= 2.6 X 10⁻²⁶ Kg

Time, T = ?

We know,

$T = \frac{2\pi m}{qB}$

Therefore,

T = 2 X 3.14 X 2.6 X 10⁻²⁶/ 2 X 0.12

T = 68 X 10⁻²⁶s

For semicircular orbit, Time taken would be T/2

T ₓ = 68 X 10⁻²⁶/2 s

T ₓ = 34 X 10⁻²⁶s

Therefore, time taken by each ion to travel the semicircular path through the magnetic field is 34 X 10⁻²⁶s.

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3 years ago

Lizard: A lizard is running in a straight line according to the following: xx(tt) = tt3⁄3 − tt2 + tt He starts at tt = 0. (a) De

insens350 [35]

Answer:

Explanation:

a ) x ( t ) = t³ / 3 - t² + t

v = dx / dt = 3 t² / 3 - 2 t + 1 = t² - 2 t + 1

b ) lizard is at rest , v( t ) = 0

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c )

velocity is positive when

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Here we see that LHS is a square so it is always positive whatever be the value of t

So velocity is always positive or lizard is always moving in positive x direction .

d ) It never moves in negative x direction .

e )

a ( t ) = dv / dt = 2t - 2

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so it has zero acceleration at t = 0 .

7 0

3 years ago

Check the correctness of formula t=2π √m/k, dimensionally​

Check the correctness of formula t=2π √m/k, dimensionally