High, low

Angular momentum

Mechanical wave

M¹L²T^-2

Scalar, vector

True

True

True

True

False

(B) 2

(c) L=rΘ

(c) both KE and PE

(a) reflection

(c) thermostat

Dimensional formula of force= [MLT^-2]

So, let a=1, b=1, c=-2

So, we have

Newton à M₁=1kg, L₁=1m, T₁=1sec

Dyne à M₂=1g, L₂= 1cm, T₂=1sec

 N₁= 1Newton

N₂= ?

Using the formula,

N₂ =  N₁ [M₁/M₂]^a [L₁/L₂]^b [T₁/T₂]^c

                = 1[1kg/1g]¹ [ 1m/1cm]¹ [1s/1s]^-2

                = 1000 g X 100 cm X 1

                    1g X 1 cm

                = 100000   = 10⁵ dynes

Since Newton’s first & third law is contained in second law, thus it may also called as real law of motion.

Derivation of 1^st law: According to Newton’s 2nd law

F= ma

Where, F is applied force, m is mass of the body & a is acceleration of body. So, in absence of force

i.e. F=0

=> ma =0

a =0 [ since m cannot equal to 0]

Zero acceleration means body at rest will remain at rest & a body in uniform motion will continue its uniform motion, which is Newton’s 1^st law of motion.

Derivation of 3rd law: Consider an isolated system of two bodies A & B. An isolated system is such that no force acts on the system.

This is Newton’s 3rd law.

Thus Newton’s 2nd law is real law of motion.

Echo is the phenomenon of repetition of sound of a source by reflection from an obstacle. It can be heard in open as well as closed spaces. Echo can only be heard when distance of source of sound & reflecting body is at least 17.2 m. Reverberation is the phenomenon of persistence or prolongation of audible sound after the source has stopped emitting sound. It is usually experienced in closed spaces.

Pressure is defined as physical force exerted on an object. The force applied perpendicular to the surface of objects per unit area. Basic formula of pressure is Force per unit area. (F/A). Unit of pressure is Pascal (Pa).

Viscosity is defined as the degree up to which fluid resists the flow under an applied force. It is measured by tangential friction force acting per unit area divided by the velocity gradient under condition of streamline flow.

Viscosity = Shear stress / Shear rate

SI unit of viscosity is m²/sec.

Coefficient of viscosity is the term to measure viscosity of given fluid. It is constant for a liquid and depends on its nature. If ‘f’ is the force of friction between two layers of fluid having area in square cm and represented by distance will have viscosity given by fµA(dv/dx)

or

f = ɳA(dv/dx)

ɳ = coefficient of viscosity

SI unit of coefficient of viscosity is Ns/m².

We have given temperature 90°F

1^st we have to convert 90°F to Celcius scale

T_(°C) = (T_(°F)-32) X 5/9

                =             (90-32) X 5/9

                =             58 X 5/9

                =             32.22°C

Now add 273 to 32.22°C to convert it into Kelvin scale

                =             32.22 + 273

                =             305.22 K

So, 90°F = 305.22 K

Free vibrations are the oscillations where the total energy remains the same over time. This means that the amplitude of vibrations stays the same.

Forced vibrations occur when an object is forced to vibrate by the means of external periodic input of force.

Resonance vibration is the forced vibration where the frequency of the vibration is very close or same to the natural frequencies of the object.

Friction is said to be natural evil because it is useful as well as harmful. Friction helps us to walk on the surface of the earth & holding the objects. Without friction many essential processes cannot be done.

On the other hand, it causes wearing & tearing in the machinery parts. It causes heat produced in moving parts due to which it also damages thing. So, it is an essential evil.

The three different modules of elasticity are

Young’s Modulus

Shear Modulus

Bulk Modulus

    Young modulus is a mechanical property that measures the stiffness of a solid material. It defines the relationship between the stress and strain in a material in the linear elasticity regime of a deformation. 

    The shear modulus (or modulus of rigidity) describes an objects tendency to shear (deform) when acted upon by opposing forces. It is defined as shear stress over shear strain.

 Shear Modulus =  

StrainThe bulk modulus of a substance is a measure of how resistant to compression that substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of volume.

Consider a body of mass m placed at point A at height h from ground.

       (i) At point A  (PE  =max, KE =0)

PE_A = mgh

KE_A = 0

Total Mechanical Energy = PE_A + KE_A

                                                                          = mgh + 0

                                                  = mgh

(ii)           AT point B

                V₁² -0 = 2gs

                V₁²  = 2gs

KE_B = 1/2m V₁² = 1/2m(2gs) = mgs

PE_B = mg(h-s)

Total Mechanical Energy = PE_B + KE_B  = mg(h-s) + mgs = mgh

(iii)          AT point C

                V²  - 0² = 2gh

                V²  = 2gh

KE_C = 1/2mv² = 1/2m(2gh) = mgh

PE_C = 0

Total Mechanical Energy = KE_C + PE_C

                                = mgh + 0

                                = mgh

So, total mechanical energy of the body at point A, B, C is same. So, total mechanical energy of the free falling body is conserved.

Pushing friction force is always greater than that of in case of pulling force. The force applied to move the body depends upon the effective weight. As effective weight in case of pulling is less than in case of pushing, so less force is required. Thus, it is easier to pull a lawn roller rather than to push it.

The phenomenon of raising the outer edge of the curved road above the inner edgeso as to provide the necessary centripetal force to the vehicles to take a safer turn & curved road is called Banking of the road. When the vehicle moves along the horizontal curved road, necessary centripetal force is supplied by the force of the friction between the wheels and surface of the road. To increase the centripetal force at the sharp edges the road is banked to avoid the skidding of the vehicles from road.

Bernoulli’s Theorm

It states that an increase in the speed of a fluid occurs simultaneously with the decrease in the pressure or decrease in fluid potential energy.

Let the viscosity, pressure and area of a fluid column at a point A be V₁, P₁, A₁  and at another point B is V₂, P₂, A_2.

Let the volume be moved from A & B to M & N.

Let AM = L₁ & BN = L₂

Now if we can compress the fluid then we have A₁L₁ = A₂L₂

Net work done per volume = P₂ – P₁

KE per volume = 1/2ρv²

KE gained per volume = ½ρ

PE gained per volume = ρ g (h₂-h₁)

Now, P₁-P₂ = 1/2P( V₂² – V₁²) + Pg (h₂-h₁)

P₁-P₂ =1/2PV₂² -1/2P₁+ Pgh₂ – Pgh₁

P₁+1/2PV₁²+Pgh1 =P₂ +1/2 PV₂²+ Pgh₂

 P + 1/2PV  + Pgh =const

This is called Bernoulli’s theorem.

The three basic modes of transfer of heat are:

1. Conduction
2. Convection
3. Radiation

1. Conduction of heat :-  It is a process in which heat is transferred from hotter part of the body to the colder part of the body without involving any actual movement of molecules in the body. Heat transfer through the process of conduction occurs in substances which are in direct contact with each other. E.g. heating one side of the needle other side also get hot. Or heat will transfer from the burner to the cooker.
2. Convection :- in this process heat will transferred in the liquid & gaseous from a region of higher temperature to the region of lower temperature due to the movement of molecules between the regions. E.g. heating of milk or boiling of milk in pan.
3. Radiation :- it is the process in which heat is transferred from one body to another body without involving molecules or medium and gets transferred in th form of radiation. E.g. heat from sun or heat from bulb.

1. We have

t =

Let us prove the correctness of the above relation using dimensional analysis

t = M°L°T¹

       = (M°L¹T°)/(M°L¹T^-2)^1/2

= (M°L°T²)^1/2

= M°L°T¹

Now we have dimensional formula for LHS & RHS

So, we get

t =

M°L°T¹ = M°L°T¹

So, the equation is correct.

Thermal expansion is the tendency of the matter to change in shape, area & volume in response to a change in temperature. The three coefficients are

Linear expansion (α) = it means change in only one direction (length).

Areal Expansion (β) = it gives change in area of a object due to change in temperature.

Volume Expansion (γ) =  it occurs in case of gases, liquids, solids. It gives change in volume w.r.t. change in temperature.

Relationship between α:β:γ = 1:2:3

Newton gave three laws of motion and are as under

1. First Law = It states that every object persists to stay at rest or in motion in a straight line if there is no external force acting on it. It is also called law of inertia.
2. Second law = It states that force is equal to change in momentum per change in time.

i.e. F = dp/dt

But p = mv [m= mass, v= velocity]

F = d(mv)/dt

   = m dv/dt  [dv/dt = a]

   = ma

i.e for constant mass m, force F equals to the mass time acceleration.

3. Third law = It states that for every action there is equal and opposite reaction.

Law of conservation of linear momentum states that the total momentum of the system is always conserved if no external force acts on an object or system of objects.

Consider two bodies A & B of masses m₁ & m₂ which are moving with velocity u₁ & u₂. After collision, velocity changes to v₁ & v₂ respectively.