Answer:
a) 
b) 
c) 
d) 
Explanation:
Average translation kinetic energy (
) is given as
....................(1)
where,
k = Boltzmann's constant ; 1.38 × 10⁻²³ J/K
T = Temperature in kelvin
a) at T = 27.8° C
or
T = 27.8 + 273 = 300.8 K
substituting the value of temperature in the equation (1)
we have

b) at T = 143° C
or
T = 143 + 273 = 416 K
substituting the value of temperature in the equation (1)
we have

c ) The translational kinetic energy per mole of an ideal gas is given as:

here
= Avagadro's number; ( 6.02×10²³ )
now at T = 27.8° C


d) now at T = 143° C


Answer:
3.38 m/s
Explanation:
Mass of child = m₁ = 25
Initial speed of child = u₁ = 5 m/s
Initial speed of cart = u₂ = 0 m/s
Mass of cart = m₂ = 12 kg
Velocity of cart with child on top = v
This is a case of perfectly inelastic collision

Velocity of cart with child on top is 3.38 m/s
Answer:
The magnitude of the force required to bring the mass to rest is 15 N.
Explanation:
Given;
mass, m = 3 .00 kg
initial speed of the mass, u = 25 m/s
distance traveled by the mass, d = 62.5 m
The acceleration of the mass is given as;
v² = u² + 2ad
at the maximum distance of 62.5 m, the final velocity of the mass = 0
0 = u² + 2ad
-2ad = u²
-a = u²/2d
-a = (25)² / (2 x 62.5)
-a = 5
a = -5 m/s²
the magnitude of the acceleration = 5 m/s²
Apply Newton's second law of motion;
F = ma
F = 3 x 5
F = 15 N
Therefore, the magnitude of the force required to bring the mass to rest is 15 N.
Answer:
Explanation:
The unknown charge can not remain in between the charge given because force on the middle charge will act in the same direction due to both the remaining charges.
So the unknown charge is somewhere on negative side of x axis . Its charge will be negative . Let it be - Q and let it be at distance - x on x axis.
force on it due to rest of the charges will be equal and opposite so
k3q Q / x² =k 8q Q / (L+x)²
8x² = 3 (L+x)²
2√2 x = √3 (L+x)
2√2 x - √3 x = √3 L
x(2√2 - √3 ) = √3 L
x = √3 L / (2√2 - √3 )
Let us consider the balancing force on 3q
force on it due to -Q and -8q will be equal
kQ . 3q / x² = k3q 8q / L²
Q = 8q (x² / L²)
so charge required = - 8q (x² / L²)
and its distance from x on negative x side = √3 L / (2√2 - √3 )
Power is the rate at which work is done (2nd option)