24. a 27-kg ball is tied to one end of a massless string of length 1.3 m. the other end of the string is tied to a nail in the center of a table. the
ball is set into uniform circular motion around the nail, and it completes one revolution every 5.2 seconds. what is the tension in the
string?
51n
44n
71n
30 n

51 N

Explanation:

The circumference of the circular path is:

C = 2πr

C = 2π (1.3 m)

C = 8.17 m

The ball travels 1 circumference in 5.2 seconds, so its speed is:

v = C / t

v = 8.17 m / 5.2 s

v = 1.57 m/s

Sum of the forces on the ball in the radial direction:

∑F = ma

T = m v² / r

T = (27 kg) (1.57 m/s)² / (1.3 m)

T = 51 N

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speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.