Answer:
A) 138.8g
B)73.97 cm/s
Explanation:
K = 15.5 Kn/m
A = 7 cm
N = 37 oscillations
tn = 20 seconds
A) In harmonic motion, we know that;
ω² = k/m and m = k/ω²
Also, angular frequency (ω) = 2π/T
Now, T is the time it takes to complete one oscillation.
So from the question, we can calculate T as;
T = 22/37.
Thus ;
ω = 2π/(22/37) = 10.5672
So,mass of ball (m) = k/ω² = 15.5/10.5672² = 0.1388kg or 138.8g
B) In simple harmonic motion, velocity is given as;
v(t) = vmax Sin (ωt + Φ)
It is from the derivative of;
v(t) = -Aω Sin (ωt + Φ)
So comparing the two equations of v(t), we can see that ;
vmax = Aω
Vmax = 7 x 10.5672 = 73.97 cm/s
Answer:
Option (a)
Explanation:
Given that,
Mass of a car, m = 1200 kg
Force exerted by the engine, F = 600 N
Noe force,F = ma
a is the acceleration of the engine

So, the acceleration of the car is 0.5 m/s².
Answer:
An engine with an electronic fuel injection system has high fuel pressure at idle because of high manifold vacuum. (option D)
Explanation:
Electronic fuel injection (EFI) system replaced carburetors back in the mid-1980s as the preferred method of supplying air and fuel to engines. The basic difference is that a carburetor uses intake vacuum and a pressure drop in the venturi, to siphon fuel from the carburetor fuel bowl into the engine. Whereas fuel injection system uses pressure to spray fuel directly into the engine.
However, under light load or at idle, a relatively high vacuum exists in the intake manifold. This means less fuel pressure is needed to spray a given volume of fuel through the injector. Under heavy load, engine vacuum drops to near zero.
Therefore, An engine with an electronic fuel injection system has high fuel pressure at idle because of high manifold vacuum.
Solution :
We know that :
Formula for Gravitational force is given by :

where, G is the gravitational constant
M is the mass of the bigger body
m is the mass of the smaller body
r is the distance between the two bodies.
And the formula for the centripetal force is given by :

where, m is the mass of the rotating body
v is the velocity
r is the radius of rotation of the body.
We know that mathematically, the gravitational force is equal to the centripetal force of the body.
Therefore,



Hence derived.