Answer:
Explanation:
Torque is defined as the cross product between the position vector ( the lever arm vector connecting the origin to the point of force application) and the force vector.
Due to the definition of cross product, the magnitude of the torque is given by:
Where 
is the angle between the force and lever arm vectors. So, the length of the lever arm (r) is minimun when 
is equal to one, solving for r:
Answer:
We know that the speed of sound is 343 m/s in air
we are also given the distance of the boat from the shore
From the provided data, we can easily find the time taken by the sound to reach the shore using the second equation of motion
s = ut + 1/2 at²
since the acceleration of sound is 0:
s = ut + 1/2 (0)t²
s = ut <em>(here, u is the speed of sound , s is the distance travelled and t is the time taken)</em>
Replacing the variables in the equation with the values we know
1200 = 343 * t
t = 1200 / 343
t = 3.5 seconds (approx)
Therefore, the sound of the gun will be heard at the shore, 3.5 seconds after being fired
Answer: The spring of the spring is 25 N/m.
Explanation:
Mass of the body = 25 g= 0.025 kg (1 kg = 1000 g)
Oscillation is 4 sec = 20
Oscillation in 1 sec =
Frequency of the vibration of the spring = 
Force constant can be calculated bu using the relation between the frequency and, mass and spring constant 'k'
The spring of the spring is 25 N/m.
Answer:
99.63 kg
Explanation:
From the force diagram
N = normal force on the worker from the surface of the roof
f = static frictional force = 560 N
θ = angle of the slope = 35
m = mass of the worker
W = weight of the worker = mg
W Cosθ = Component of the weight of worker perpendicular to the surface of roof
W Sinθ = Component of the weight of worker parallel to the surface of roof
From the force diagram, for the worker not to slip, force equation must be
W Sinθ = f
mg Sinθ = f
m (9.8) Sin35 = 560
m = 99.63 kg
Answer:
C) 20 m/s
Explanation:
Wave: A wave is a disturbance that travels through a medium and transfers energy from one point to another, without causing any permanent displacement of the medium itself. Examples of wave are, water wave, sound wave, light rays, radio waves. etc.
The velocity of a moving wave is
v = λf ............................ Equation 1
Where v = speed of the wave, λ = wave length, f = frequency of the wave.
Given: f = 2 Hz (two complete cycles in one seconds), λ = 10 meters
Substituting these values into equation 1
v = 2×10
v = 20 m/s.
Thus the speed of the wave = 20 m/s
The right option is C) 20 m/s
