Answer:
Ratio of length will be 
Explanation:
We have given time period of the pendulum when length is
is 
And when length is
time period 
We know that time period is given by

So
----eqn 1
And
-------eqn 2
Dividing eqn 2 by eqn 1

Squaring both side

Answer:
option (b)
Explanation:
According to the Pascal's law
F / A = f / a
Where, F is the force on ram, A be the area of ram, f be the force on plunger and a be the area of plunger.
Diameter of ram, D = 20 cm, R = 20 / 2 = 10 cm
A = π R^2 = π x 100 cm^2
F = 3 tons = 3000 kgf
diameter of plunger, d = 3 cm, r = 1.5 cm
a = π x 2.25 cm^2
Use Pascal's law
3000 / π x 100 = f / π x 2.25
f = 67.5 Kgf
Answer:
Our solar system has total eight planets out of which four are inner planets and four are outer planets. The four outer planets are Jupiter, Saturn, Uranus and Neptune. The common characteristics of outer planets is that they are gaseous planets. They are larger on size than the inner rocky planets and are faraway from Sun. They have larger period of revolution around the Sun.
Uranus is a gaseous planet and lies far from Sun and hence has large period of revolution. It takes 84 Earth years to revolve around Sun. This data indicates that Uranus resides in the outer region of the Solar System.
The relationship between resistance R and resistivity

is

where L is the length of the wire and A its cross section.
The radius of the wire is half the diameter:

and the cross section is

From the first equation, we can then find the length of the wire when

(copper resistivity:

)
Answer:
The amount of heat required is 
Explanation:
From the question we are told that
The mass of water is 
The temperature of the water before drinking is 
The temperature of the body is 
Generally the amount of heat required to move the water from its former temperature to the body temperature is

Here
is the specific heat of water with value
So

=>
Generally the no of mole of sweat present mass of water is

Here
is the molar mass of sweat with value
=> 
=> 
Generally the heat required to vaporize the number of moles of the sweat is mathematically represented as

Here
is the latent heat of vaporization with value 
=> 
=> 
Generally the overall amount of heat energy required is

=> 
=> 