Answer:
Explanation:
Answer:
Explanation:
mass of book, m = 2.10 kg
diameter of pulley, = 0.170 m
radius of pulley, R = 0.085 m
mass of hanging book, m' = 3 kg
initial velocity, u = 0 m/s
distance, s = 1.2 m
time, t = 0.9 s
Let a be the acceleration of the system and T and T' is the tension in the string which is horizontal and vertical respectively.
Use second equation of motion
s = ut + 0.5 at²
1.2 = 0 + 0.5 x a x 0.9 x 0.9
a = 2.96 m/s²
(a) Use second equation of motion
T = ma
T = 2.10 x 2.96
T = 6.216 N
m'g - T' = m'a
3 x 9.8 - T' = 3 x 2.96
T' = 20.52 N
(b) Let the moment of inertia of the pulley is I.
So, (T' - T)R = I x α
(20.52 - 6.216) x 0.085 = I x 2.96 / 0.085
I = 0.035 Kgm²
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<span>A.
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Answer
given,
Length of the string, L = 2 m
speed of the wave , v = 50 m/s
string is stretched between two string
For the waves the nodes must be between the strings
the wavelength is given by
![\lambda = \dfrac{2L}{n}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cdfrac%7B2L%7D%7Bn%7D)
where n is the number of antinodes; n = 1,2,3,...
the frequency expression is given by
![f = n\dfrac{v}{2L}](https://tex.z-dn.net/?f=f%20%3D%20n%5Cdfrac%7Bv%7D%7B2L%7D)
now, wavelength calculation
n = 1
![\lambda_1 = \dfrac{2\times 2}{1}](https://tex.z-dn.net/?f=%5Clambda_1%20%3D%20%5Cdfrac%7B2%5Ctimes%202%7D%7B1%7D)
λ₁ = 4 m
n = 2
![\lambda_2 = \dfrac{2\times 2}{2}](https://tex.z-dn.net/?f=%5Clambda_2%20%3D%20%5Cdfrac%7B2%5Ctimes%202%7D%7B2%7D)
λ₂ = 2 m
n =3
![\lambda_3 = \dfrac{2\times 2}{3}](https://tex.z-dn.net/?f=%5Clambda_3%20%3D%20%5Cdfrac%7B2%5Ctimes%202%7D%7B3%7D)
λ₃ = 1.333 m
now, frequency calculation
n = 1
![f = n\dfrac{v}{2L}](https://tex.z-dn.net/?f=f%20%3D%20n%5Cdfrac%7Bv%7D%7B2L%7D)
![f_1 =1\times \dfrac{50}{2\times 2}](https://tex.z-dn.net/?f=f_1%20%3D1%5Ctimes%20%5Cdfrac%7B50%7D%7B2%5Ctimes%202%7D)
f₁ = 12.5 Hz
n = 2
![f = n\dfrac{v}{2L}](https://tex.z-dn.net/?f=f%20%3D%20n%5Cdfrac%7Bv%7D%7B2L%7D)
![f_2 =2\times \dfrac{50}{2\times 2}](https://tex.z-dn.net/?f=f_2%20%3D2%5Ctimes%20%5Cdfrac%7B50%7D%7B2%5Ctimes%202%7D)
f₂= 25 Hz
n = 3
![f = n\dfrac{v}{2L}](https://tex.z-dn.net/?f=f%20%3D%20n%5Cdfrac%7Bv%7D%7B2L%7D)
![f_3 =3\times \dfrac{50}{2\times 2}](https://tex.z-dn.net/?f=f_3%20%3D3%5Ctimes%20%5Cdfrac%7B50%7D%7B2%5Ctimes%202%7D)
f₃ = 37.5 Hz