Answer:
Magnetic field, B = 0.004 mT
Explanation:
It is given that,
Charge, 
Mass of charge particle, 
Speed, 
Acceleration, 
We need to find the minimum magnetic field that would produce such an acceleration. So,

For minimum magnetic field,



B = 0.004 T
or
B = 4 mT
So, the magnetic field produce such an acceleration at 4 mT. Hence, this is the required solution.
Pitch of the sound increases as frequency increases.
choose B pitch
Answer:
The speed of the bat is 5.02 m/s.
Explanation:
Given that,
Frequency = 30.0 kHz
Frequency of echo = 900 Hz
We need to calculate the frequency
Using formula of beat frequency

Put the value into the formula



We need to calculate the speed of the bat
Using Doppler equation

Put the value into the formula







Hence, The speed of the bat is 5.02 m/s.
Answer:
a. 37.75°
b. 6.21 m
Explanation:
a. The horizontal force acting on a pendulum bob is given as:
F = mgsinθ
where m = mass of bob
g = acceleration due to gravity
θ = angle string makes with the vertical or angle of displacement
Making θ subject of formula, we have:
θ = 
θ = 
θ = 37.75°
The maximum angle of displacement is 37.75°
b. Period of a pendulum is given as:

where L = length of string
Therefore, making L subject of formula:


The string holding the pendulum has to be 6.21 m long.
Answer:
Explanation:
Work done by the spring is negative .
Work done by force F creating displacement d is given by the following expression .
Work = F x d
Both force and displacement are vector quantity .
When direction of force and direction of displacement is same , work is positive . When direction of force and direction of displacement is opposite , work is negative .
When spring is compressed , it exerts a restoring or opposing force in a direction opposite to the direction of displacement of box . Hence here force is opposite to displacement . Restoring force acts opposite to displacement . Hence work done by spring on box is negative .