I know you are Indian by your question, HC Verma class 9 or 11 !!
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Answer:
v = 2.21 m/s
Explanation:
The foreman had released the box from rest at a height of 0.25 m above the ground.
We need to find the speed of the crate when it reaches the bottom of the ramp. Let v is the velocity at the bottom of the ramp. It can be calculated using conservation of energy as follows :

So, its velocity at the bottom of the ramp is 2.21 m/s.
<span>14 m/s
Assuming that all of the energy stored in the spring is transferred to dart, we have 2 equations to take into consideration.
1. How much energy is stored in the spring?
2. How fast will the dart travel with that amount of energy.
As for the energy stored, that's a simple matter of multiplication. So:
20 N * 0.05 m = 1 Nm = 1 J
For the second part, the energy of a moving object is expressed as
KE = 0.5 mv^2
where
KE = Kinetic energy
m = mass
v = velocity
Since we now know the energy (in Joules) and mass of the dart, we can substitute the known values and solve for v. So
KE = 0.5 mv^2
1 J = 0.5 0.010 kg * v^2
1 kg*m^2/s^2 = 0.005 kg * v^2
200 m^2/s^2 = v^2
14.14213562 m/s = v
So the dart will have a velocity of 14 m/s after rounding to 2 significant figures.</span>
Answer:
Isothermal : P2 = ( P1V1 / V2 ) , work-done 
Adiabatic : : P2 =
, work-done =
W = 
Explanation:
initial temperature : T
Pressure : P
initial volume : V1
Final volume : V2
A) If expansion was isothermal calculate final pressure and work-done
we use the gas laws
= PIVI = P2V2
Hence : P2 = ( P1V1 / V2 )
work-done :

B) If the expansion was Adiabatic show the Final pressure and work-done
final pressure

where y = 5/3
hence : P2 = 
Work-done
W = 
Where 
Answer:
0.5 m
Explanation:
Givens:
ym1 = 2.5 mm
ym2 = 4.5 mm
Ф_1=π / 4
Ф_2=π / 2
We have 2 ways to solve this problem. The first one given that the 2 waves have the frequency then we know that the resultant wave amplitude is
Ym = (ym1 + ym2)cos(Ф_2/2)
By substitution we have
Ym= (0.025 + 0.045)cos(π/4) = 0.496 m
The second one is it treat them as Phasors where the phase between them is Ф_2=π / 2 Therefore
Ym^2=(ym1^2+ym2^2)
So we have Ym=√0.025^2+0.045^2
= 0.5 m