Choice of frame of reference
One of the problems that a student faces is about choosing the frame of reference while solving a problem. A frame of reference in which the motion is simpler has to be chosen. In the figure above, the motion of mass m in the ground frame is much complicated as compared with its motion in the frame of reference attached to M. Of course the frame attached to M is non-inertial. Hence proper pseudo force has to be used.
Conservation laws
A block of mass m is pushed towards a wedge of mass M and height H as shown. What should be the horizontal velocity u so that the block reaches the top of the wedge? All the surfaces are smooth and the wedge surface becomes vertical at the top.
Also understand how simple would be the problem if the wedge were to be fixed.
S.H.M
Find the natural frequency of the system shown in the figure. All the pulleys are smooth, massless and frictionless.
C = Q/V
You know that capacitance of a capacitor is C = Q/V
Imagine a parallel plate capacitor with two plates A and B as shown. What would you think is Q if you want to write the potential difference V ? Q1 or Q2 or Q3 or Q4
concentric shells
There are 4 concentric shells A, B, C and D of radii a, 2a, 3a and 4a respectively. Shells B and D are given charges q and -q respectively. Shell C is now earthed. Find the potential difference between the shells A and C.
Impulse
In the pulley system shown, a particle of mass m falls from a height H onto the mass m and gets stuck with it at t = 0. Find the value(s) of t at which the two blocks are in the same horizontal level.
Reminds you of friction
- If F < µmg, find the direction and magnitude of the frictional force acting on the sphere.
- Find the maximum value of F so that the sphere will not slip.
Tension in the string
Two masses are connected with an inextensible massless string as shown that passes over a frictionless pulley and through a slit as shown. The string is vertical on either sides of the pulley. A constant force of friction equal to 10 N acts on the string because of its contact with the slit as it passes through it. Then
(a) 4 kg mass has an acceleration of 5/3 ms-2 downwards
(b) tension in the string is same throughout
(c) force exerted on 2 kg body by the string is 70/3 N
(d) if the blocks are interchanged in position, 2 kg body moves up with an acceleration of 10/3 ms-2
Concept of Pseudo force
A bob is hanging over a pulley inside a car. The other end of the string is in the hands of a person standing in the car. The car is moving horizontally with an acceleration 'a' towards right as shown. The person is pulling the string down with an acceleration 'a' relative to the car. What is the tension in the string ?
Rigid body concept
A rod AB is shown in the figure. End A of the rod is fixed on the ground and end B is instantaneously in contact with the block which is moving with velocity v = 31/2 m/s. The velocity of end B of the rod when the rod makes an angle of 600 with the ground is ?
* If a body is rotating about a stationary axis passing through its center of mass, its angular momentum about any point in space is same, that is spin angular momentum is an intrinsic property of a body.
Beauty of Work-Energy Theorem
A particle can slide along a track with elevated ends and a flat central part as shown. The flat part has a length L. The curved portions of the track are frictionless but the flat part has a coefficient of kinetic friction of 0.20
The particle is released from rest at a point A, which is at a height of L /2 above the flat part of the track. Where does the particle finally stop?
E.M.I
The arrangement is in a magnetic field 
ABCD is a square frame of mass M and side 'a' and resistance R. There is no effect of magnetic field on the other block of mass m. (M > m) From the time of release, find the magnitude and direction of the current in the frame as a function of time. Also find the time after which the block attains half the maximum speed that it could attain.
1-D Motion .
1. A balloon is moving up vertically such that if a stone is thrown from it with a horizontal velocity vo relative to it, the stone always hits the ground at a fixed point (2 vo2/g) distance horizontally away from it. Find the height of the balloon as a function of time.
Collision
A sphere of mass m falls vertically with a velocity v on a smooth inclined wedge of mass M at rest on a smooth horizontal surface. Find the velocity of the wedge immediately after the collision which is elastic.
misconcept on work done
The work done by a force acting on a body is the dot product of the force and the displacement of the body is wrong.
Work done by the force is the dot product of force and displacement of point of application of the force is correct.
charge resides on the outer surface
Which charge resides on the outer surface of the conductor?
Is it that all the protons come to the surface?
Do all the electrons come to the surface? No?
Then do you think all the free electrons come to the surface?
Equivalent Capacitance
Find the equivalent Capacitance between A and B where the resistances marked are in ohms and capacitances are in micro farads.
An enigmatic doubt
The question goes like this. A force of 10 N holds a spring in the compressed state. If the spring constant is 20 N/m what is the elastic potential energy stored in the spring?
The argument which made the doubt enigmatic is as follows:
Excellent problem on W-E theorem
A block of mass m is rigidly connected with a smooth plank by a spring of constant k. If the plank is moved with a uniform velocity V0 by an external agent, find the work done by him till the spring gets compressed maximum.
wheatstone-network
I found this interesting. Given resistance A is greater than B.Does the current flow from a to d or d to a in the connecting wire that connects the points a and d.
Time constant of R-C circuit
C1 = 2C2. At t = 0, C1 was charged to a potential of V and switch was closed. Find the time constant of the circuit and current immediately after closing the switch.
Heat conduction
This is a beautiful problem that one should understand.
Three rods of identical cross section and made up of the same material are used to form an isosceles triangle ABC right angled at B as shown. The ends A and B are maintained at temperatures T and T(2)1/2 while the steady state temperature of C is TC. Find TC/T assuming only heat conduction to take place.
multiconceptual problem
A block is attached to the ceiling by a spring of constant k = 200 N/m. A conducting rod is also rigidly attached to the block. The combined mass of the block and the rod is 0.3 kg. The rod can slide on vertical rails without friction.The distance between the rails is L = 1 m. A capacitor of capacitance C = 500µF is attached to the rails by connecting wires as shown. The entire system is in a uniform magnetic field B = 20 T directed into the paper. Find the angular frequency in rad/s of vertical oscillations of the block.Neglect self inductance and electrical resistance of the rod and all wires.
(A) 20(5)1/2 (B) 20 (C)(20/3)(5)1/2 (D) none
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