Answer:
Explanation:
For an electric force, F the formula:
F = kQq/r^2
Given:
r2 = 1/2 × r1
F1 × r1 = k
F1 × r1 = F2 × r2
F2 = (F1 × r1^2)/(0.5 × r1)^2
= (F1 × r1^2)/0.25r1^2
= 4 × F1.
Answer: 0.61 s
Explanation:
Given
Mass of object, m = 0.015 kg
Radius of object, r = 0.055 m
Acceleration of object, g = 9.8 m/s²
In a pendulum,
T = 2π * √[I /(mgd)]
The moment of Inertia, I of a hollow sphere is given by
I(sphere) = 2/3MR² + MR²
I(sphere) = 5/3MR²
Also, d = R
Substituting these into the first equation, we have
T = 2π * √[(5/3MR²) / (mgr)]
T = 2π * √[(5/3r) / (g)]
T = 2 * 3.142 * √(5/3 * 0.055) / (9.8)]
T = 6.284 * √(0.092/9.8)
T = 6.284 * √0.00939
T = 6.284 * 0.097
T = 0.6095 s
To 2 significant figures,
The period is 0.61 s
Answer:
Explanation:
First of all we shall calculate the velocity of composite mass . Let it be v . Applying law of conservation of momentum
mu - MU = ( m + M ) v
v = mu - MU / ( m + M )
loss of kinetic energy
= 1/ 2 mu² + 1/2 MU² - 1/2 ( M +m ) v²
= 1/ 2 mu² + 1/2 MU² - 1/2 ( M +m ) (mu - MU)² / ( m + M )²
= 1/ 2 mu² + 1/2 MU² - 1/2 (mu - MU)² / ( m + M )
= 1/2 [ m²u² + mMu² +mMU² + m²U² - m²u² - M²U² - 2 muMU ] / ( m + M )
= 1 / 2 [ mMu² + mMU² - 2 muMU ] / ( m + M )
= 1 / 2mM [ (u² + U² - 2 uU) / ( m + M )]
= 1/2 mM x k
where
k = [ (u² + U² - 2 uU) / ( m + M )]
Given
m = .004 kg
M = 4 kg
u = 890 ms⁻¹
U = 7 ms⁻¹
k = ( 890² + 7² - 2 x 890 x 7 ) / 4.004
= ( 792100 + 49 - 12460 ) / 4.004
= 194727.52
loss of kinetic energy
= 1/2 mM x k
= .5 x .004 x 4 x 194727.52
= 1557.82 J .
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