FIIT JEE STUDY MATERIAL " ELECTRICITY "Full description
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A bloc block k of mass mass m is res resti ting ng on the the roug rough h hori horizo zonta ntall gro ground und.. Mini Minimu mum m forc forcee requ requir ired ed to move move it is
3mg
(a)
2.
5
. Then coefficient of friction is
1
(b)
5
4
(c)
5
(a) Pe
(c)
5.
(b)
t
P 1
c1 e
dN dt
4
3 4
t
is
(c)
The The ef effecti ective ve resi resist stan ancce bet betwe ween en A & B of the shown network. Where resistance of each resistor is R, is (a)
4.
(d)
A nu nucleus wh whose de decay constant is is is produced at a constant rate of P nuclei per second. if N is the no. of nuclei present after time t then
3.
1
8R
(b)
11 6R
P t
e t
(d) none of the above
A
B
6R 11
(d) none of these
5
A pote potent ntio iome mete terr wir wiree AB as sh shown own is is 40 40 cm cm lon long g of resistance 50 50 / m free end of an ideal voltmeter is touching the potentiometer wire. What should be the velocity veloc ity of the jockey as a function of time so that reading in voltmeter is varying with time as (2sin t ) (a) 10 sin tcm/s (b) 10 cos tcm/s (c) 20 sin t cm/s (d) 20 cos tcm/s
10
10 v
A
B
4v
A resi resist stor or of of resis resista tance nce R, R, capaci capacitor tor of capa capacit citan ance ce C and and induc inductor tor of indu induct ctanc ancee L are are conn connect ected ed in parallel to AC power source of voltage 0 sin t . The maximum current through the resistance is half of the maximum current through the power source. Then value of R is 3 (a) C 1 L (c) 5
6.
1 L C
(b)
3 L
1 C
(d) none of these
An real real object object of 2cm 2cm leng length th is placed placed uprigh uprightt at a dista distance nce of x cm from from a spher spherica icall mirr mirror or with with its base on the principl principlee axis its image image is formed formed at distance distance x + 20 cm. The image image is real real inverted inverted & 4 cm in length. Find focal length of spherical mirror. mirror. (a) 30 cm (b) 40/3 cm (c)40 cm (d) 30/4 cm
7.
A sample of an ideal gas is taken through a cyclic process whose P-V graph is in the shape of the rectangel consisting of isochoric and isobaric process. If maximum pressure of the gas is P0. The value of minimum presure of the gas so that efficiency of cycle is 20% , is (a) 0.2 P0 (b) 0.4 P0 (c) 0.8 P0 (d) data insufficient
8.
One end of ideal string tied up with fixed support & other end is tied with a bob. The string is released from horizontal position. When string makes an angle of with vertically downward direction then the acceleration vector of bob is horizontal. Then is (a)tan -1(1)
9.
(c)
mg
2
2 r
AY mgr
(b)
(d)
AY
mg 2 AY
(c)
r24 r 14
G H J Kb gg
4 3
c
3 2
3 1
r r
2
- - - - - - - - - - - -
)
< r > m
r 2
AY
hb gg
(b)
(d)
2 3
4 3
hb g
c
r23 r13 g g
r 2
r24 r 14
G Hr r J Kb gg 2
1
A semicircular ring of radius R carrying current i is placed in a magnetic field B so that it is perpendicular to magnetic field as shown. Net force acting of the ring is (a) 2BiR (b) 2BiRsin (c) 2BiRcos
(d) BiR sin
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x ------------------------------ -
A projectile is projected at some angle from the horizontal in a vertical plane. Then the angular momentum of the projectile about point of projection is proportional to tn where t is time then n is equal to (a) 1/2
13.
(d) none of these
mg 2
(a) 3 r2 r 1
12.
d3i
Two solid spherical balls of radius r 1 & r 2(
4
11.
(c) tan-1
A massless string of length l , cross-sectional area A and Young’s modulus Y is tied up with a bob of mass m. The bob is moving with constant angular speed in circular path of radius r as shown. Find elongation in the string assuming <
10.
(b) tan-1(1/2)
(b) 1
(c) 1
1 2
(d) 2
A cylindrical ice of radius r 1 and length l & of relative density 0.9 is initiallly floating in the container
of radius r 2(>r 1) containing water. A body of relative density 2 is placed on the top surface of ice so that ice is just submerged. The increase in the water level is (a)
9
r 12
G H
10 r22 r 12
(b)
9 r 1
2
GJ H
10 r 2
(c)
r 12
G H
(d)
10 r22 r 12
r 1
2
GJ H
10 r 2
14.
A charged capacitor o fcapacitance C & having charge Q is to be connected with another uncharged capacitor of capacitance C’ as shown so that till the steady state is reached, find the value of C’ if heat librated through the wires is maximum. (a) zero (b) C (c) C/2 (d) 2C.
15.
The electric field of a light wave at a point is E= (100 N/c) sin (3x 1015t)sin (6x 1015t) where t is time in second. This light falls on a metal surface having work function of 2 eV, then maximum possible kinetic energy of photoelectrons is about (a)16 eV (b) 7 eV (c) 6 eV (d) 4 eV
16.
Inclined plane AB & BC are at an inclination of 600 &300 from the horizontal respectively. Two projectiles are thrown from A& C such that they strikes at B with same speed. The length AB is
1
m and length BC is 1m. If projectile from A is thrown with speed 2 m/s then the initial speed 3 of projectile thrown from C is (a) 1/2 m/s (b) 1 m/s (c) 2 m/s (d) none of these 17.
Three charges q, q and -2q are fixed on the vertices of an equilateral triangular plate of edge length a. This plate is in equilibrium between two very large plates having surface charge density 1 and 2 respectively. Find the period of small angular oscillation about an axis passing through its centroid and perpendicular to plane. Moment of inertia of the system about this axis I.
0I 2 (a) q a 1 2 2 0I
(c) 2
18.
0I 2 (b) 2 q a 1 2 2 0 I (d) 2 q a 1 2
3q a 1 2
A Particle is executing linear SHM. Its displacement from mean position, velocity & acceleration at an instant are x, v and a respectively. Find amplitude of the motion. (a) x
v2 2a
(b)
2
x
xv2 a
x
(c)
Fv I sinG Hax 2
(d) none of these
19.
A solid sphere of uniform density has radius equal to R. it has a cavity of radius R/2 such that the centre of mass lies on the surface of the cavity. Find distance between centre of sphere and centre of cavity. (a) Zero (b) R/14 (c) R/6 (d) none of these
20.
Find the moment of inertia of a semicircular ring of mass M and
radius R about an axis which is tangent to it and perpendicular to the line joining its ends. (a) (c)
21.
MR 2
(b) MR 2
2 3
MR 2
2
- - - - - - - - - - - - - - -
(d) none of these
A container contains two immiscible liquids of density 1 and 2 ( 2 1 ). A capillary of radius r is inserted in the liquid so that its bottom reaches upto denser liquid and lighter liquid does not enters in to the capillary. Denser liquid rises in capillary and atain height equal to h which is also equal tocolumn length of lighter liquid. Assuming zero contact angle find surface tension of heavier liquid. (a)
22.
r 2 gh
(b) 2 r 2 gh
2
v 2 v 0 cv
G (a) G G H
26.
b ggh 2
g
(d) 2 r 2 1 gh
1
J J J K
(b)
cv G Hv (v / 2) J Kv
0
(c)
c ( v / 2) G Hc v J Kv
(d)
0
cv G Hc v / 2 J Kv
0
Gm 2
d2 1i
(b)
R
Gm 2 R
(c)
d2 1i
Gm
(d) none of these
R 2
An infinitely long cylindrical radiation source is radiating with power of W watts per unit of its length. The intensity of radiation, at a distance r from the axis of the cylinder is proportional to. (a)
25.
2
2
A particle of mass m is placed at a distance R from centre of a uniformly dense thin ring of mass m and radius R on a n axis passig through its centre and perpendicular to its plane. Find the speed of the particle when it reaches at the centre of the ring due to their mutual gravitation force. (a)
24.
r
h
Three bodies A, B and C are situated at the vertices of an equilateral triangle ABC at t = 0. Each of the particle moves with constant speed v. A always has its velocity along AB, B along BC a& C along CA. During its journey A emit whistle of high frequency v0. Find frequency heard by B considering speed of sund equal to c. c
23.
(c)
1
1 r
(b)
1 2
r
(c)
1
(d) ln r
r
A point object is placed in air at a distance d from the pole of a refracting convex surface on its principal axis & it starts moving with speed v perpendicular to its principle axis as shown in figure. Find the speed of its image if the radius of the convex surface is d. (a) 0.5 v (b) 1.5 v (c) 2v (d) 3v
1
15 .
O
An infinitely long current carrying wire carrying current i. A charge of mass m & charge q is
projected with speed v parallel to direction of current at a distance r from it. Then the radius of curvature at point of projection is 2 rmv (a)
27.
q 0 i
2 rmv (b)
q 0 i
(c) r
(d) cannot be determined
In a region at a distance r from z-axis magnetic field B B0 rtk is present where B0 is constant t is time. Then the magnitude of induced electric field at a distance r from z-axis is given by (a)
28.
r 2
B0
(b)
r 2 2
B0
(c)
r 2 3
B0
(d) none of these
A small square loop of edge length a and resistance R is moved with velocity v0 away from an infinitely long current carrying conductor carrying current i so that the conductor and side of square are always in same plane. Find induced current in loop at a separation of r. (a)
0 ia 2 v r 2 R
(b)
0ia 2 v 4 r 2 R
(c)
0ia 2 v
(d)
2 r 2 R
0 iav 2 rR
29.
Current in a X-ray tube operating at 40 kV is 10 mA. 1% of the total kinetic energy of electrons hitting the target is converted into X-rays. Then the heat produced in the target per second is (a)396J (b) 4J (c) 400J (d) can not be determined
30.
What is the minimum value of applied force F so that both the block lifts up. Consider string to be ideal and pulley to be massless & frictionless (a) 4g (b) 8g (c) 5g (d) 7g
