A pulley system has a velocity ratio of 4 and an efficiency of 90%. Clculate:
i) the mechanical advantage of the system.ii) the effort required to raise a load of 300 N by the system.
V.R. = 4, η = 90%, Load = 300 N
Name the type of single pulley that can act as a force multiplier. Draw a labelled diagram of the above named pulley.
Single movable pulley:
Give one use each of the electromagnetic radiations given below:
ii) Ultraviolet radiations
iii) Infrared radiation.
i) Microwaves are used for communication.
ii) Ultraviolet rays are used for sterilizing purposes.
iii) Infrared waves are used for therapeutic purposes.
Show that for the free fall of a body, the sum of the mechanical energy at any point in its path is constant.
Let a body of mass m fall freely under gravity from height h above ground.
Let, A B and C be the positions of body.
Let x be the distance fallen from A to B.
At position A:
K.E= 0 (body is at rest)
P.E = mgh
Total energy = 0 + mgh = mgh … (i)
At position B:
Let v1 be velocity of body, then u = 0
Using equation of motion, we have
V2 = u2 + 2as
V12 = 0 + 2 gx
V12 = 2 gx
At position C:
Let velocity of body be v.
Then, u = 0 and S = h
V2 = u2 + 2gs
V2 = 0 + 2gh
V2 = 2gh
Therefore, from equations (i), (ii) and (iii), it is clear that the sum of mechanical energy remains same at any point in the path of free fall of a body.
Explain why musical instruments like the guitar are provided with a hollow box.
Musical instruments like guitar are provided with a hollow box so that when the strings are set into vibration, forced vibrations are produced in box. Since the box has a large area, it sets a large volume of air into vibration which produces a loud sound of same frequency as that of the string.
Mention any two difference between the mass and weight of a body.
Difference between mass and weight of the body:
1. It is a scalar quantity.
2. It is the quantity of matter contained in a body.
1. It is a vector quantity.
2. It is the force with which the earth attracts a body.
Define Newton, the S.I. unit of force. State its relationship with the C.G.S. unit of force.
One Newton is the amount of force required to produce an acceleration of 1 m/s2 in a body of mass 1 kg.
1 Newton = 1 kg x 1 m/s2
= 1000 g x 100 cm/s2
= 105 g cm/s2
= 10 5 dyne
That is, 1 N = 105 dyne
State the amount of work done by an object when it moves in a circular path for one complete rotation. Give a reason to justify your answer.
The amount of work done will be equal to zero. This is because, work is said to be done only when there is a displacement produced. In case of a body moving in a circular path, the body comes to its original place, therefore, there is no displacement and hence work is zero.
Calculate the height through which a body of mass 0.5 kg should be lifted if the energy spent for doing so is 1.0 Joule.
Mass, m = 0.5 kg
P.E = 1.0 g
Acceleration due to gravity, g = 10 m/s2P.E = mgh
A uniform metre scale is kept in equilibrium when supported to the 60 cm mark and a mass M is suspended from the 90 cm mark as shown in the figure. State with reasons, whether the weight of the scale is greater than, less than or equal to the weight of mass M.
Let the load be M.
Load of the arm, dL = (90 – 60) = 30 cm
Since, weight of the scale will act at the centre of gravity of scale which is mid-point of the scale (i.e., 50 cm mark)
Effort arm, dE = 60 – 50 = 10 cm
Let weight of the scale be W.
By principle of moments,
L × dL = E × dE
M × 30 = W × 10
W = 3 M
Therefore, since weight of the scale is three times that of M.
So, weight of the scale is greater than the weight of M.