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Study of light
Optics
Two supplementary units in SI system
radian, steradian
Distance is always greater than or equal to displacement .Is this statement True or False
True
The slope of position - time graph gives --------
Velocity
If x= bt2,find the dimensions of b, when x is measured in metre and t in second .
L T -2
Is it possible for a body to have zero velocity with non zero acceleration. Give an example.
Yes,when a body is thrown upwards, at the highest point of projection, velocity is zero, but acceleration is g.
The velocity- time graph of an object in uniform motion is --------'
A straight line parallel to the time axis
What are the values of components of velocity at the highest point of projection?
vx = v0 Cosθ, vy = 0
State Newton's second law of motion.
The rate of change of momentum of a body is directly proportional to the applied force, and the change takes place in the direction of force.
What are the expressions for the Time of Flight (T) and the Maximum Height attained(H) by a projectile in projectile motion?
T = 2 v0 Sinθ /g,
H = v02 Sin2θ/2g
If y = (3)1/2 x - 20 x2,find the angle of projection.
θ = 60°
The expression for Optimum speed of a car to avoid wear and tear of the tyres on a banked road is ---------
v = ( Rg tanθ)1/2
Define coefficient of friction.
u = f / N
Expression for maximum safe speed of a car on a level road is -------------
v = (uS R g)1/2
A car travels from A to B at 60 km/ hr and returns to A at 90 km/hr.What is the average speed?
72 km/ hr
2v1 v2 / v1 + v2
Find the recoil velocity of a gun, having mass equal to 5 kg, if a bullet of 0.025 kg acquires the velocity of 500 m/s after firing from the gun .
V = - 2.5 m/s
V = - mv / M
A 30 W motor is used to lift a crate up into the air,such that it rises at 0.5 m/s.How much does the crate weigh?
60N
F=P/v
A light body and a heavy body have same momenta,which one has greater kinetic energy?
Light body
K= p2/ 2m
The expressions for torque are-------,------,---------
T= r×F = dL/dt = Iα
A solid sphere is rotating about a diameter at an angular velocity w. If it cools so that the radius reduces to 1/n of its original value,then its new angular velocity becomes -----
w' = n2 w
L = Iw = 2MR2w/5
L= I'w' = 2M(R/n)2w'/5 =
L/L = w'/n2w or n2w = w'
A coin is rolling on a plane surface.Find its total kinetic energy.
3mv2/ 4
Total KE = Translational KE + Rotational KE = mv2/2 + Iw2/2
= mv2/2 + 1/2 . mR2/2. v2/ R2
= mv2/2 + mv2/4= 3mv2/4
Derive the expression for acceleration due to gravity below the surface of earth.
What is the value of acceleration due to at the centre of earth?
g (h) = g (1- d/R)
g = GM/R2,g(d) = GM/(R - d)2
M = 4πR3ρ/3 , m = 4π(R- d)3ρ/3
m = M( R - d)3 / R3
g(d) = GM(R - d)3/R3( R - d)2
= GM(R - h)/R3 = g(1 - h/R)
Prove law of conservation of energy in the case of freely falling body.
At point A, TE = mgH
At point B, TE = mgh +mvh2/2
= mgh+mg(H - h) = mgH
At point C, TE = mvH2/2 = mgH
Derive the Displacement-Time relation using graph
Velocity time Graph
Area under v- t graph = Displacement
S= Rectangle area+ Triangle area
S= ut+ (v-u)t/2 = ut+ at2/2