Show the equation of simple pendulum to be dimensionally consistent

1 answer:

nataly862011 [7]3 years ago

6 0

T is in seconds (s)

2pi is dimensionless 

L is in meters (m) 

g is in meters per second squared (m/s^2) 

so you can write the equation for the period of the simple pendulum in its units... 

s=sqrt(m/(m/s^2)) 

simplify

s=sqrt(m*s^2*1/m) cancelling the m's 

s=sqrt(s^2) 

s=s 

therefore the dimensions on the left side of the equation are equal to the dimensions on the right side of the equation.

You might be interested in

A regulation basketball has a 15 cm diameter and may be appropriated as a thin spherical shell.

REY [17]

Solution :

From the given data,

For the spherical shell is $\frac{k^2}{R^2}= \frac{2}{3}$

where x is the radius of gyration and the acceleration of a rolling body on an inclined plane = a

Therefore,

$a =\frac{g \sin \theta}{1+ \frac{k^2}{R^2}}$

$= \frac{g \sin \theta}{1 +\frac{2}{3}}$

$= \frac{3}{5} g \sin \theta$

= 0.6 x 9.81 x sin ( 29.7)

$= 2.913 \ m/s^2$

$h = \frac{1}{2} a(\Delta t)^2$

$\Delta t = \sqrt{\frac{2h}{a}}$

$\Delta t = \sqrt{\frac{2 \times 2.9}{2.913}}$

Δt = 1.411 s

6 0

3 years ago

Different structural forms of the same element are called

julia-pushkina [17]

Answer:

allotropes

Explanation:

4 0

3 years ago

A car traveling with constant speed travels 150 km in 7200 s what is speed of the car

spayn [35]

The speed of the car is exactly 150/7200 km/sec, or 125/6 meters/sec.

In more familiar units, that speed is equivalent to ...

-- (20 and 5/6) meters/sec

-- 75 km/hour

8 0

3 years ago

An ideal gas occupies 600 cm3 at 20c. at what temperature will it occupy 1200 cm3 if the pressure remains constant? 10c 40c 100c

Anna11 [10]

ANS : 313℃
You need to use K in this.
To convert ℃ to Kelvin (K), add 273.15 to ℃.