Answer:
The correct answers are
(a) It decreases to 1/3 L
(ii) is (c) It is constant
Explanation:
to solve this, we list out the number of knowns and unknowns so as to determine the correct equation to solve the problem
The given variables are as follows
Initial volume V1 = 1L
V2 = Unknown
Initial Temperature T1 = 300K
let us assume that the balloon is perfectly elastic
At 300K the balloon is filled and it stretches to maintain 1 atmosphere
at 100K the content of the balloon cools reducing the excitement of the gas content which also reduces the pressure, however, the balloon being perfectly elastic, contracts to maintain the 1 atmospheric pressure, hence the answer to (ii) is (c) It is constant,
For (i) since we know that the pressure of the balloon is constant
by Charles Law V1/T1 =V2/T2
or V2 = (V1/T1)×T2 =
× 
= 
× L = L/3 hence the correct answer to (i) is 1/3L
Answer:
The tension is 
Explanation:
The free body diagram of the question is shown on the first uploaded image From the question we are told that
The distance between the two poles is 
The mass tied between the two cloth line is 
The distance it sags is 
The objective of this solution is to obtain the magnitude of the tension on the ends of the clothesline
Now the sum of the forces on the y-axis is zero assuming that the whole system is at equilibrium
And this can be mathematically represented as
To obtain 
we apply SOHCAHTOH Rule
So 
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![= tan^{-1} [\frac{1}{7}]](https://tex.z-dn.net/?f=%3D%20tan%5E%7B-1%7D%20%5B%5Cfrac%7B1%7D%7B7%7D%5D)
Answer:
3.63 s
Explanation:
We can solve the problem by using the equivalent SUVAT equations for the angular motion.
To find the angular acceleration, we can use the following equation:
where
is the final angular speed
is the initial angular speed
is the angular distance covered
is the angular acceleration
Re-arranging the formula, we can find :
Now we want to know the time the bit takes starting from rest to reach a speed of 
. So, we can use the following equation:
where:
is the angular acceleration
is the final speed
is the initial speed
t is the time
Re-arranging the equation, we can find the time:
Answer:
Explanation:
Force between two charges of q₁ and q₂ at distance d is given by the expression
F = k q₁ q₂ / d₂
Here force between charge q₁ = - 15 x 10⁻⁹ C and q₃ = 47 x 10⁻⁹ C when distance between them d = (1.66 - 1.24 ) = .42 mm
k = 1/ 4π x 8.85 x 10⁻¹²
putting the values in the expression
F = 1/ 4π x 8.85 x 10⁻¹² x - 15 x 10⁻⁹ x 47 x 10⁻⁹ /( .42 x 10⁻³)²
= 9 x 10⁹ x - 15 x 10⁻⁹ x 47 x 10⁻⁹ /( .42 x 10⁻³)²
= 35969.4 x 10⁻³ N .
force between charge q₂ = 34.5 x 10⁻⁹ C and q₃ = 47 x 10⁻⁹ C when distance between them d = ( 1.24 - 0 ) = 1.24 mm .
putting the values in the expression
F = 1/ 4π x 8.85 x 10⁻¹² x 34.5 x 10⁻⁹ x 47 x 10⁻⁹ /( .42 x 10⁻³)²
= 9 x 10⁹ x - 34.5 x 10⁻⁹ x 47 x 10⁻⁹ /( .42 x 10⁻³)²
= 82729.6 x 10⁻³ N
Both these forces will act in the same direction towards the left (away from the origin towards - ve x axis)
Total force = 118699 x 10⁻³
= 118.7 N.
Explanation:
We have,
Length of a metal rod is 55 cm or 0.55 m
Change in length is 0.2 cm or 0.002 m
It is required to find the change in temperature of a metal rod. The coefficient of linear expansion is given by :
is the change in temperature
So, the change in temperature is 303.03 degrees Celsius.
