The angular momentum of the person is given by:

where

is the mass of the person,

is the tangential velocity, and

is the distance of the person from the center of rotation. Using these data, we find
Answer:
Explanation:
a )
Force at the surface = FR
Value of g at height h = g( 1 - 2 h / R )
force at height h = F_R ( 1 - 2 h / R)
F_R / 2 = F_R ( 1 - 2 h / R)
= F_R - 2 F_R xh / R
F_R / 2 = 2 F_R x h / R
1 / 2 = 2h / R
4h = R
h = R / 4 . Ans
b )
Value of g at depth d = g( 1 - d / R )
force at depth d = F_R ( 1 - d / R)
F_R / 2 = F_R ( 1 - d / R)
= F_R - F_R xd / R
F_R / 2 = F_R x d / R
1 / 2 = d / R
2d = R
d = R / 2
Answer:
2.0 m
Explanation:
Energy is conserved.
Initial KE = Final PE + Work done by friction
½ mv² = mgh + Fd
½ mv² = mgh + mgμd
½ v² = gh + gμd
½ v² − gh = gμd
d = (½ v² − gh) / (gμ)
d = (½ (7.5 m/s)² − (10 m/s²) (2.1 m)) / ((10 m/s²) (0.35))
d = 2.0 m
Answer:
Explanation:
The magnetic field is pointing upwards , so magnetic flux is upwards . Due to increase in area , magnetic flux in upward direction will increase . Hence according to Lenz's law , induced current will be such that it will try to counter this increase . It is possible if current is in clockwise direction . Due to it magnetic field will be induced in downward direction thus reducing the total magnetic flux.
Hence direction of induced current will be clockwise direction in the loop as shown in the image enclosed .
The centripetal acceleration is calculated using the following rule:
C = (v^2) / (r)
where:
C is the centripetal acceleration = 6.54 g = 6.54 * 9.8 = 64.092 m/sec^2
v is the speed of the centrifuge that we want to calculate
r is the radius of radius (length of centrifuge arm) = 15 m
Substitute with the givens to get the speed as follows:
64.092 = (v^2) / 15
v^2 = 961.38
v = 31.006 m/sec