The period T of a pendulum is given by:
where L is the length of the pendulum while
is the gravitational acceleration.
In the pendulum of the problem, one complete vibration takes exactly 0.200 s, this means its period is
. Using this data, we can solve the previous formula to find L:
Answer:
The maximum amount of work is
Explanation:
From the question we are told that
The temperature of the environment is
The volume of container A is
Initially the number of moles is
The volume of container B is
At equilibrium of the gas the maximum work that can be done on the turbine is mathematically represented as
Now from the Ideal gas law
So substituting for in the equation above
Where R is the gas constant with a values of
Substituting values we have that
Answer:
(a)
(b)
(c) K.E. = 21.168 J
(d)
Explanation:
Given:
- mass of a block, M = 3.6 kg
- initial velocity of the block,
- constant downward acceleration,
That a constant upward acceleration of is applied in the presence of gravity.
∴
- height through which the block falls, d = 4.2 m
(a)
Force by the cord on the block,
∴Work by the cord on the block,
We take -ve sign because the direction of force and the displacement are opposite to each other.
(b)
Force on the block due to gravity:
∵the gravity is naturally a constant and we cannot change it
∴Work by the gravity on the block,
(c)
Kinetic energy of the block will be equal to the net work done i.e. sum of the two works.
mathematically:
K.E. = 21.168 J
(d)
From the equation of motion:
putting the respective values:
is the speed when the block has fallen 4.2 meters.
Explanation:
It is given that,
Velocity in East,
Velocity in North,
(a) The resultant velocity is given by :
(b) The width of the river is, d = 80 m
Let t is the time taken by the boat to travel shore to shore. So,
t = 16 seconds
(c) Let x is the distance covered by the boat to reach the opposite shore. So,
x = 48 meters
Hence, this is the required solution.