Answer:
6.13428 rev/s
Explanation:
= Final moment of inertia = 4.2 kgm²
I = Moment of inertia with fists close to chest = 5.7 kgm²
= Initial angular speed = 3 rev/s
= Final angular speed
r = Radius = 76 cm
m = Mass = 2.5 kg
Moment of inertia of the skater is given by
In this system the angular momentum is conserved
The rotational speed will be 6.13428 rev/s
Answer:
answer a) 2
Explanation:
Assuming stationary state, following Fourier's law:
Q = A*k* dT/dL
where Q= heat flow , A= cross sectional area, dT/dL= temperature gradient along the bar
if the cross sectional area is doubled , then the gradient is the same ( since the heat sources do not change in temperature or position , and the length of the bar is the same). Since the gradient is same , the temperature is the same under stationary conditions , then we can assume k remains constant in the cross section.Therefore
Q₁= A₁*k* dT/dL
Q₂= A₂*k* dT/dL
dividing both equations
Q₂ / Q₁ = A₂/A₁ = 2
then the correct answer is a)
Note:
Since the cross sectional area is doubled, then heat loss to the surroundings will be
Q loss= h* A exposed * ΔT
then
Q loss₂ / Q loss ₁ = A exposed ₂/ A exposed ₁
for a circular cross section or a squared cross section
A exposed ₂/ A exposed ₁ = √2
then
Q loss₂ / Q loss ₁ = √2
therefore we did not take into account the increase in heat loss due to the increased in exposed area to the environment
Answer:
261.3 m/s
Explanation:
Mass of bullet=m=15 g=
1 kg=1000g
Mass of block=M=3 kg
d=0.086 m
Total mass =M+m=3+0.015=3.015 kg
K.E at the time strike=Gravitational potential energy at the end of swing
Using g=
Substitute the values
Velocity after collision=V=1.3 m/s
Velocity of block=v'=0
Using conservation law of momentum
Using the formula
The magnetic flux through an area A is given by
where
B is the magnitude of the magnetic field
A is the area
is the angle between the direction of B and the perpendicular to the surface A.
In our problem, the area lies in the x-y plane, while B is in the z direction, this means that B and the perpendicular to A are parallel, so
and
, so we can rewrite the formula as
We can calculate the area starting from the radius:
And then using the intensity of the magnetic field given by the problem,
, we find the magnetic flux: