Answer:
u = 3.35 m/s
Explanation:
given,
mass , m = 0.455 kg
R = 0.675 m
Height of Loop = 1.021 m
the speed required at the top of loop be v
equating the force vertically


v² = 6.622
v = 2.57 m/s
Let the initial speed of ball be u
using conservation of energy

where, 



0.7 u² = 7.85092
u² = 11.2156
u = 3.35 m/s
the initial speed is 3.35 m/s
Answer:
vi) Double the current in the wire, and double the number of turns in the 20-cm long solenoid
Explanation:
The magnetic field inside the solenoid and the current flowing in the coil of solenoid are related to each other by the following equation
B₀=μ₀nI₀
Where,
B₀ is the magnetic field in the middle of solenoid
n is the number of turns in the coil of solenoid
I₀ is the current flowing in the coil of solenoid
In the above equation, as μ₀ is a constant so the magnetic field will be directly proportional to the number of turns multiplied by the current. So, changing the radius of the coil or length of the coil will have no effect on the magnetic field.
As we have to increase the magnetic field by 4 times, we need to double the current as well as the number of turns as mentioned in the option vi.
Answer:
The kinetic energy of the mass at the instant it passes back through the equilibrium position is 0.06500 J.
Explanation:
Given that,
Mass = 2.15 kg
Distance = 0.0895 m
Amplitude = 0.0235 m
We need to calculate the spring constant
Using newton's second law

Where, f = restoring force


Put the value into the formula


We need to calculate the kinetic energy of the mass
Using formula of kinetic energy

Here, 

Here, 


Put the value into the formula


Hence, The kinetic energy of the mass at the instant it passes back through the equilibrium position is 0.06500 J.
The basic definition of pressure is force/area and the scientific community defined that as the Pascal (Pa).