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On tripling the speed of motion of a body, the change in K.E. is:
K.E. ∝ v^{2}
So when v → 3v, K.E. → 9K.E.
The moon revolves around the earth due to the gravitational force (F) of the earth on the moon. The work done by the gravitational force is (r = radius of the circular orbit of moon):
An electric bulb of 60 W is used for 5 hours a day. The cost of electricity involved in a month of 30 days at Rs. 3.00 per unit is (in Rs):
Cost of Electricity = P*t*cost per kW
=0.06 kW x (5 x 30) x 3= Rs. 27
A body is moved through a distance of 3 m in the following different ways. In which case is the maximum work done?
Work done = Mgh
Work will be maximum when the change in height is maximum, thus when it is lifted vertically upward.
A: 50 kg man climbing a ‘slant length of 5 m along a 30° incline.
B: 25 kg man running with 2 m/s speed.
C: A force of 5 N acting on an object moving with 5 m/s speed for 5 min.
If the energies in A, B and C are E_{A}, E_{B} and E_{C} respectively, then:
E_{a} = mv^{2}/2 = 50 x 10 x 5sin30º = 250j
E_{b} = mv^{2}/2 = 25 x 4/2 = 50j
E_{c} = fvt = 5 x 25 x 60 = 7500j
Therefore, E_{b} < E_{a }< E_{c}
Two bodies of equal weight are kept at heights of h and 1.5 h, respectively. The ratio of their potential energies is:
Potential energy is mathematically defined as, P.E = mgh
Potential energy of body 1 = P.E_{1} = mgh_{1}
Potential energy of body 2 = P.E_{2} = mgh_{2}
Since weight of two bodies are equal, therefore, P.E_{1} / P. E_{2} = h / 1.5 h = 2:3
If a force of F newton moves a body with constant speed v, the power delivered by it is:
Given: Velocity = v & Force = F
We know that work done is equal to the product of force and displacement.
W = F*d
Dividing by t on both sides then we get:
W/t = F*d/t
d/t = v ( Speed = Distance/ Time)
W/t = P (Power)
Therefore, P = F*v
Potential energy is energy stored in matter. Joule is the SI unit of energy.
A mass ‘m’ falls from a height ‘h’ any point on its path the total energy is:
Work = Force * Displacement (Nm)
If the bulbs of 60 W and 40 W are connected in series to a 220 V source the bulb which glows brighter is:
A porter with a suitcase on his head is climbing up a flight of stairs with a uniform speed. The work done by the ‘weight of the suitcase’ on the suitcase is:
Force and displacement are in the same direction.
So, the work done is positive.
Two bodies of unequal masses are dropped from a cliff. At any instant, they have equal:
They will have the same acceleration due to gravity because it is independent of mass.
Two masses m and 2m are dropped from a certain height ‘h’. Then on reaching the ground:
A person A does 500 J of work in 10 minutes and another person B does 600 J of work in 20 minutes. Let the power delivered by A and B be P_{A} and P_{B} respectively. Then,
Power = P = Energy/Time = Work/Time
P_{A}= 500/10*60 = 0.83J/s
P_{B}= 600/20*60 = 0.5J/s
P_{A }> P_{B}
In the case of negative work, the angle between the force and displacement is:
One unit of electricity is consumed by,
A: P = 40 W bulb used for t = 25 hours
B: P = 20 W bulb used for t = 50 hours
Both A and B are true as, energy E in kWh is best related as:
The work done on an object does not depend upon the______.
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