Unit & Dimensions Questions and Answers

A particle is acted upon by a force of com magnitude which is always perpendicular t elocity of the particle The motion of the pa akes place in a plane It follows that its velocity is constant its acceleration is constant its kinetic energy is constant hover in straight line

The velocity of sound in a solid is given as v kYapb where K is a dimensionless quantity Y is young s modulus of elasticity and p is density of material What is the value of a and b Given Y ML 1 T 2 A a 1 b 1 B a 1 b 1 1 a 1 b 2 Ca D a 1 b 1 2

s 5 29 The dimension of the quantity to he electron h Planck s constant and c velocity of ligh a M L T A c ML T A2 b MOLTA d IM L TA 30 A projectile is thrown with an initial is e chargest You

b RT where p is pressure v is specific volume T is temperature and R is characteristic gas constant The SI unit of a is P v 1 J kg K 2 m kg 3 m5 kgs C

d The frequency of sound as heard by the observ standing on the platform will decrease 5 A rocket is moving at a speed of 220 m s towards a stationary target emits a sound of frequency 1000 Hz Some of the sound reaching the target gets reflected back to the rocket as an echo The frequency of the echo as detected by the rocket is Take velocity of sound 330 m s a 3500 Hz b 4000 Hz c 5000 Hz d 3000 Hz

32 If m e and h denote mass of electron charge of electron electric permittivity and Planck s me4 2 2 constant respectively The unit of e a energy c force More than One Correct Options is same as b power d pressure

c la then H E a length c time d If E M J and G denote energy mass angular momentum and gravitational constant respectively EJ M G has the dimensions of 12 b mass d angle

30 The density of a material in CGS system of units is 4 g cm In a system of units in which unit length is 10 cm and unit of mass is 100 g the value of density of material will be a 0 04 c 40 31 Tf b 0 4 d 400

A force of 200 N acts on a body If the unit of mass and length is doubled and unit of time halved then the numerical value of this force in the new system becomes 25 12 5 37 5 50

31 If m e o h and c denote mass of electron charge of electron Planck s constant and speed of light respectively The dimensions of me h c a M L T c M LT 32 If m e en and h denote mass of plonton are b M L T d M LT

One side of a cube is measured as a 4 00 1 The volume of the cube will be 64 0 1 16 0 1 64 0 3 16 0 3

A uniform wire of length L and mass M is stretched between two fixed points keeping a tension F A sound of frequency is impressed on it Then the maximum vibrational energy is existing in the wire when A B 1 ML 21 L FL M C 2x FM F 2 V ML

Three infinitely charged sheets are kept parallel to x y plane having charge densities as shown Then the value of electric field at P is 40 A 0 20 0 C K K B 40 K 0 D 20 0 Z 3a Z 2a Z 0 N P O 20

A point charge Q 1 C is fixed at the centre of an insulated disc of mass 1 kg The disc is resting on a rough horizontal surface Another charge Q 1 uC is fixed vertically above the centre of disc at a heighth 1m The disc is displaced slightly in horizontal direction by a small displacement x Friction is sufficient to prevent slipping Let radius of disc be R and the corresponding angular displacement of disc is 0 X If angular acceleration is a y x 10 0 rad sec then find y z R h 1m DE sufficiently rough

A thin convex lens made from crown glass 2 has focal length f When it is measured in two different liquids having 5 refractive indices and it has the focal 4 3 lengths f and f respectively The correct relation between the focal lengths is 2014 1 f and both become negative 2 f f f 3 f f and f becomes negative 4 f f and f becomes negative

A student performs an experiment with a simple pendulum and reads the time for 25 oscillations If he would have recorded the time for 200 oscillations the error in the measurement of time period would have reduced by a factor of 8 20 O 10 5

Asin Bx Ct then dimensions of is s is the displacement of the particle given as s A C B which is at x x at any time t 1 MLT 1 3 MLT 2 M L T 4 ML T 2

87 A non conducting wire is bent into a semi circle of radius R and a charge Q is uniformly distributed over it as shown in the figure Find the ratio EA at the other end A of diameter AB that bisects the wire as shown in the figure a R c R In 1 2 Q B x x A b 2R d 2RIn 1 2

Two bodies A and B of equal mass moving with equal speeds along X and Y axes of a rectangular coordinate system collide and stick together They will move in a direction inclined to X axis at an angle of a 30 b 60 c 45 d 90

51 A body of mass m is kept on a rough inclined plane of inclination 45 with horizontal If the body remains at rest on the inclined plane then reaction force by the plane on the body is 1 mg sin45 2 mg cos60 3 mg 4 mg 2

Planck s constant h speed of light in vacuum c and Newton s gravitational constant G are three fundamental constants Which of the following combinations of these has the dimension of length hG hG 3 2 5 2 a c hc b d Gc 1 3 2 NEET II 2016

onductivity is A the same as resistivity it is just more convenient to use for good conductors 3 expressed in 2 1 C equal to 1 resistance D expressed in 2 m 3 not a meaningful quantity for an insulator ep

3m s V 4m s a 2m s and a 1m s The rate of change of speed at this moment is 1 A system of mixture of 20 moles of Argon and 10 moles of carbon monoxide gas SQ DU SW undergo a slow thermodynamics process given by 4 2 3 Here 8Q represents infinitesimally small amount of heat supplied to he gas du represents infinitesimally small amount of change in internal energy of the gas mixture and sw represents infinitesimally small amount of work done by the gas 5X mixture The molar specific heat capacity of the mixture for this process is where 7Y X and Y are smallest possible integers Find X Y 2 If ring of radius R is placed on smooth floor connected by a string at the top Other end of string is connected to upper plate of capacitor of same mass M and charge density and area A Lower plate of capacitor is rigidly fixed Then which of the

Percentage error in measuring the radius and mass of a solid sphere are 1 and 2 respectively The error in measurement of moment of inertia about its diameter is 0 9 O 6 O 5 O 4 Marks 4 1

Two materials of dielectric constants k and k are introduced to fill the space between the two parallel plates of a capacitor as shown in figure The capacity of the capacitor is A 2 A 2 Question Type Single Correct Type 1 2 A 0 K K 2d 2AE0 d K K K K 3 AG d AEO K K

14 The graph shown in the diagram represents the variation of temperature 7 of the bodies x and y having same surface area with time t due to the emission of radiation Find the correct relation between the emissivity and absorptivity of the two bodies power 2003 2M T XX a E E and a a ay and a a b E E Ex Ey c E E Ey and a ay d E E and a ay T 00 4 t

6 A disc D of mass m 4 0 kg is tied at one end of a cord of length 1 1 0 m other end of which is fixed at the centre of a large circular platform The platform is maintained horizontal and rotated about its vertical axis of symmetry The disc is placed on the platform as shown How long after the disc is placed will the cord break The maximum tensile force the cord can withstand is Tmax 100 N and coefficient of kinetic friction between the dise and the platform is 0 1 D

Graph of position of image vs position of point object from a convex lens is shown Then focal length of the lens is JEE 2006 d 2 d t dv A 0 50 0 05 cm V u u cm wy 31 1 b 30 20 B 0 50 0 10 cm du 10 tr 31 v cm 30 20 10 017 47 0 0 C 5 00 0 05 cm 0 1 su 4 U 10 V 10 1 1 1 10 10 b s D 5 00 0 10 cm 1 1 2 2 1 u 0 1 6 d b D

3 0 40 4 1 A convex lens a glass slab a glass prism and a solid sphere all are made of the same glass the dispersive power will be 1 In the glass slab and prism 2 In the lens and solid sphere 3 Only in prism 4 In all the four Sn AN 002 16 The refracting ang of material of pris deviation is 1 180 3A 3 90 A A ray of light tr medium The cr maximum poss T C 1 2 3 2C 1 45m

Assuming that the volume of a liquid flowing per second V through a cylindrical tube depends on i the pressure gradient P ii the radius of the tube and iii the coefficient of viscosity of liquid n Find by the method of dimension how it depends on these quantities

In an experiment the following observation s were recorded L 2 820 m M 3 00 kg I 0 087 cm Diameter D 0 041 cm Taking g 9 81 m s using the 4MgL formula Y the maximum TD 1 permissible error in Y is 1 7 96 2 4 56 3 6 50 4 8 42

Which of the following is correct A dimensionally incorrect equation may be correct A dimensionally correct equation must be physically correct Derived quantities may have dimensions in terms of the base quantities A unitless quantity may have a nonzero dimension

In an experiment four quantities a b c and d are measured with percentage error 1 2 3 and 4 respectively Quantity P is calculated as follows Flights cd a 7 error in Pis b 4 c 14 d 10

Question 9 Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity In one such system dimensions of different quantities are given in terms of a quantity X as follows position X speed X acceleration XP linear momentum X force X Then a a p 2B b p q r c q r a d p q r B

If the size of atom is in the range of 10 10 m to 10 m is scaled up to the tip of sharp pin assume tip of pin to be in the range of 10 6 to 10 5 m Roughly size of nucleus is NCERT Pg 20 1 0 1 A 2 0 01 A 3 0 001 4 10

Example 91 If two resistors of resistances R 4 0 5 and R 16 0 5 2 are connected i in series and ii ir parallel find the equivalent resistance in each case with limits of percentage error

A packet contains silver powder of mass 20 23 g 0 01 g Some of the powder of mass 5 75 g 0 0 01 g is taken out from it The mass of the powder left back is 1 14 48 g 0 00 g 2 14 48 0 02 g 3 14 5 g 0 1 g 4 14 5 g 0 2 g

In the formula X 3YZ X and Z have dimensions of capacitance and magnetic induction respectively What are the dimensions of Y in MKSQ system Q is the charge 1 M 7 0 2 M 14Q4 3 M 2 7 0 4 M 7 04

A body of mass 5 kg is suspended by a spring balance on a smooth inclined plane as shown in figure The reading of the spring balance will be g 10 m s 5 kg mmmm 30 50 N 25 N 25 3 N 25 2 N TTT

Two iron blocks of equal mass but having different surface area slide down on same inclined plane with coefficient of friction u If first block with surface area A experience a frictional force f then the second block with surface area 2A will experience frictional force f 712

In a screw gauge 5 complete rotation of the screw gauge it to move a linear distance of 0 25cm There are 100 circular scale divisions The thickness of a wire measured by this screw gauge gives a reading of 4 main scale division and 30 circular scale division Assuming negligible zero error the thickness of the wire is Question Type Single Correct Type 1 2 3 0 430 cm 0 215 cm 0 315 cm

Q A vernier callipers has its main scale of 10 cm equally divided into 200 equal parts Its vernier scale of 25 divisions coincides with 12 mm on the main scale The least count of the instrument is a 0 020 cm c 0 010 cm b 0 002 cm d 0 001 cm

A curved section of a road is banked for a speed V If there is no friction between road and tyres of the car then 1 car is more likely to slip at speeds higher than v than speeds lower than v car cannot remain in static equilibrium on the curved section 3 car will not slip when moving with speed v 4 None of the above

A flat plate moves normally with a speed vl towards a horizontal jet of water of uniform area of cross section The jet discharges water at the rate of volume V per second at a speed of v2 The density of water is p Assume that water splashes along the surface of the plate at right angles to the original motion The magnitude of the force acting on the plate due to the jet of water is A B pVv1 pV v V pV 21 22 P v V Un 2 V v 2

amusement park A machine in an consists of a cage at the end of one arm hinged at O The cage revolves along a vertical circle of radius r ABCOEFGH about its hinge O at constant linear speed v gr C The cage is so attached that the man of weight w standing on a weighing machine inside the cage is always vertical Then which of the following is correct a The reading of his weight on the machine is the same at all positions b The weight reading at A is greater than the weight read ing at Eby 2 w c The weight reading at G w d The ratio of the weight reading at E to that at A 0

Find the current through the battery as a function of time Initially the switch K is open and S is closed At time t 3RC switch S is opened and switch K is closed Calculate the heat dissipated in the resistors after very long time R www R www C R K www C OS

Which among the following is correct O Joule Coulomb x Volt Joule Volt x Ampere O Joule Coulomb Volt O Volt Joule x Coulomb

40 A point object is kept in front of a plane mirror The plane mirror is doing SHM of amplitude 2 cm The plane mirror moves along the x axis which is normal to the mirror The amplitude of the mirror is such that the object is always in front of the mirror The amplitude of SHM of the image is a O b 2 cm c 4 cm d 1 cm

ColumnI L Torque II Power of lens III Plane angle IV Angular frequency Column I MOLOTO MOL TO ii ii MOLOT 1 iv M L T 2 16 Which of the following shows the correct matching in terms of dimensionally simillar quantity as x in e a 1 i R c III i R IV iii S b II iii S d 17 Which of the follwoing will remain unaffected if mass and length of the body changes a III 1 R b IV iii S c 1 iv Q d Both a and b 18 The dimensions of physical quantity X in the equation 1 X Angular frequency Angular velocity is same as a II i R b IV i R Column III P Wave number Q Moment of force R s Angular velocity c III 1 R d 1 i P

Magnetic field due to a long solenoid of cross 2 section 15 cm is 200 T This solenoid crosses a square coil of area 2m at its center such that length of solenoid is parallel to the axis of coil then magnetic flux linked through the square coil is 1 Zero 2 0 1 Wb 3 02 Wh A