Unit & Dimensions Questions and Answers

For a body moving along x axis the distance travelled by body from a reference point is given as function of time t as x a b where a and bi are constant then the dimension of ab is same as 1 Speed 2 Acceleration 3 Distance 4 Angular velocity In a thermodynamic process helium gas obeys the

The unit of length velocity and force are doubled Which of the following is the correct change in the other units Correct Answer A Unit of time is doubled B Unit of mass is doubled c Unit of momentum is doubled

A physical quantity x depends on quantities y and z as follows x Ay B tan Cz where A B and Care constants Which of the following do not have the same dimensions a x and B b c y and B A Cand z x and A 1

0 E m I and G denote energy mass angular momentum and universal gravitational constant respectively then has the dimensions of 2 Mass 1 Length 3 Time 4 Angle 146 kl work is performed in order to com El m G

A physical equation is given by v a 4 e where v is speed x is displacement and t is time The dimensions of 32 will be O MLT 2 M L T 2 M L T 2 O M L 2T

Dimensions of resistance in an electrical circuit in terms of dimension of mass M of length L of time T and of current I would be AIPMT Prelims 2007 1 ML T 1 4 2 ML T 1 3 ML T 2 4 ML T 11 11

18 The density of a material in CGS system of unit is 4 g cm In a system of units in which unit C length is 10 cm and unit of mass is 100 g th value of density of material will be 1 400 3 0 4 AIPMT Mains 201 2 0 04 4 40

1 10 You measure two quantities as A 1 0 m 0 2 m B 2 0 m 0 2 m We should report correct value for VAB as Final Results FS S 38 1 4 m 0 2 m 23 1 4 m 0 3 m 31 1 4 m 0 4 m 8 1 41 m 0 15 m

Question 35 Assertion Some of readings taken using an instrument may be more and some of readings may be lesser than the actual value of the physical quantity Reason Instrumental errors are random errors If both Assertion and Reason are true and reason is the correct explanation of assertion If both assertion and reason are true and Reason is not correct explanation of assertion assertion is true but reason is false Both assertion and reason are false

3 Pv14 4 Pv T 7 If unit of mass is assumed as 10 kg unit of length 20 m and unit of time as 50 s Then the value of 1 newton of force in new system of units is 1 10 3 25 2 12 5 4 20

Fortnightly Test TYMRG1 FT02 Code A In the following questions 21 to 23 a statement of assertion A is followed by a statement of reason R 1 If both Assertion Reason are true and the reason is the correct explanation of the assertion then mark 1 2 If both Assertion Reason are true but the reason is not the correct explanation of the assertion then mark 2 3 If Assertion is true statement but Reason is false then mark 3 4 If both Assertion and Reason are false statements then mark 4 21 A Force cannot be added to pressure R They have same dimensions

a 22 V V P In the equation pressure and V is volume Then the dimensional formula of a is 1 ML T 2 3 ML T 2 V b RT P is 2 ML T 2 4 ML5T 2

Product of Vectors The angles which i j 2k makes with x axis y axis and z axis respectively are A 60 60 and 45 B 60 45 and 45 C 45 45 and 45 1 D 60 60 and E

If resultant of two vectors A and B is perpendicular to B If A 4 3 B TL A Angle betweenA and B is radian B Magnitude of resultant is 2 3 C B A B 0 D Angle between A B and A is acute angle

Which of the following statement is not true 1 Numerical constants cannot be deduced by the method of dimensions 2 The equations containing trigonometric functions cannot be derived by the method of dimensions 3 If the dimensional formula of a physical quantity is given then physical quantity may or may not be unique 4 The method of dimensions can be used to derive relations other than product of power functions

Baahubali developed a new type of a missile in which thrust dimension of force is provided due to ejection of gases with some velocity He knows that thrust depends on rate of density change volume of gas ejected and velocity with which it was ejected relative to missile If velocity of efflux and volume of gas ejected efflux both are doubled while rate of density change is halved by what factor will the thrust change

24 If vectors cos coti sin ootj and B cosi sin t J CO 2 2 are functions of time then the value of t at which they are orthogonal to each other are 2015 Re a t 0 b t TC 40 c t TC 20 d t

A LT B L C T D LT T If K represents kinetic energy V represents velocity and T represents time and these are chosen as th fundamental units then the dimensional formula of surface tension is Given surface tension is force pe unit length A IKY T 1 B IKYT21 C IK YT D KYTI

In a new system of units called royal system of units units of length mass and time are each ten times of respective SI units The unit of force is this system will be A equal to that in SI system B 10 times that of SI system C 100 times that of SI system D 1000 times that of SI system

Q 13 Least counts of 3 measuring instruments A B and Care 5 x 10 3 m 5 x 10 3 cm and 5 x 10 mm respectively Which one is more precise AE A Instrument C C Instrument A B Instrument B D Both A and B

Q 8 Assertion A In a given number 0 07203 the underlined zeroes are not significant AE Reason R If the number is less than 1 the zero s on the right of decimal point but to the left of the first non zero digit are not significant

Speed of particle is given as v Ae Bt Where t is time then A and B are respectively A LT T B L T C T LT D LT T

Force on a particle is given by F a log Bxt where t is time and x is distance then a and B are respectively A LT LT B MLT2 LT C ML T dimensionless D MLT2 dimensionless

Significant figures 23 The volume of a cube having sides 1 2 m is appropriately expressed as 1 1 728 x 106 cm 3 1 8 x 106 cm 2 1 7 106 cm 4 1 73 106 cm

Which of the following quantities cannot enter into the list of fundamental quantities in any system of units A Length mass and velocity B Mass time and acceleration C Mass velocity and time D Force momentum and time

Q No 14 A protector in slip gauges is provided to A Protect slip gauges when not is use B Take up all the wear when in use C Clean the slip gauges D Facilitate wringing of slip gauges

A wave function expressing the displacement y as a function of its position x and time is given as y Plog Qx e R Which of the following expressions has dimensions different from other 1 yR 3 KIC R 2 PR 4 QR

Out of the following pairs which one does not have identical dimensions a Moment of inertia and moment of a force b Work and torque c Angular momentum and Planck s constant d Impulse and momentum

If dimensions of length are expressed as Gh where G c and h are the universal gravitational constant speed of light and Planck s constant respectively then 1 a x 2 1 b x 2 2 3 c x 2 d x 1 2 2 2 3 2 N z 1 2 1 2 2 1 2 N I 2

20 The velocity v of a particle at time t is b where a b and care t c constants The dimensions of a b and care a L LT and LT 2 b LT 2 L and T c L T and LT 2 d LT 2 LT and L given by v at 2006

3 The density of a material in CGS system of units is 4 g cm In a system of units in which unit of length is 10 cm and unit of mass is 100 g the value of density of material will be a 0 04 b 0 4 c 40 d 400 Mains 2011

3 1 764 x 10 cm 4 176 40 cm If force F Energy E and velocity v are taken as fundamental quantities then the dimensional formula of length L is 1 FEv 3 F E v 2 FEv 4 F E v

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle The motion of the particle takes place in a plane It follows that 1 its velocity is constant 2 its K E is constant 3 its acceleration is constant 4 it moves in a straight line

a 1 c 1 1 If a simple pendulum is taken to a place where g decreases by 2 then time period UP CPMT 2012 a increase by 5 b increase by 1 c increase by 2 d decrease by 5 Th Th a simple pendulum executing SHM falls freely support then Te BCECE 2012

A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity n flowing per second through a tube of radius r and length and having a pressure difference Pacross its ends is f V 3 V Pr 8n 8Pm 2 V M 8Pr4 n 4 V 3 2 4

If the velocity v of a particle is related with bx x and t as v ax where a b c are c t constant and x is in meter and t is in second then find the dimensions of b A LT C L T B LT D LT 7 X cx X Les SHI N c b uel R A LT C LT v x bx c t B LT D LT

D B 1 The resultant of two forces F and F is P If F is reversed then resultant is Q Then the value of P Q in terms of F and F is A 2 F F B F F C F F D none of these 31 D B FF P F Gazial aia al full on Q4 d P Q You A 2 F F C F F B F F D

In the figure shown battery 1 has emf 6V and internal resistance 102 Battery 2 has emf 2V and internal resistance 3 2 The wires have negligible resistance What is the potential difference across the terminals of battery 2 192 www 392 000NL

If in relation y A sin Bx Ct x and y is in meter and t is in second then dimensions of are A LT C LT B LT D T L 9 aoi y A sin Bx Ct 4i x 4 y la C All A LT C LT 10 y x x c B LT D T L 204

A conducting square loop of side 1 and resistance R moves in its plane with a uniform velocity v perpendicular to one of its side A magnetic induction B constant in time and space pointing perpendicular and into the plane of the loop exists everywhere The current induced in the loop is Blv A clockwise B C R Blv R 2B v R anticlockwise anticlockwise

The length breadth and thickness of a block are given by 1 12 cm b 6 cm and t 2 45 cm The volume of the block according to the idea of significant figures should be 1 1 x 102 cm 2 2 x 10 cm 162 m3

4 The velocity v of a particle at time t is given te where a b and c are constants The dimensions of a b and e are respectively 1 LT 2 L and T 2 L T and LT 3 LT LT and L 4 L LT and T by v at

6 If force F velocity V and time T are taken as fundamental units then the dimensions of mass are 1 F VT 3 F V T Write the mancion 2 F VT 4 F V T Rowar 43 44

4 Let denote the dimensional formula of the permittivity of the vacuum and that of the permeability of the vacuum If M mass L length T time and I electric current then a M L T 1 b M L T412 c M MLT 21 2 d g ML T 1 UT 1998

4 May have a nonzero dimension 23 In a particular system the units of length mass and time are chosen to be 10 cm 10 g and 0 1 s respectively The unit of force in this system will be equal to 1 0 1 N 2 IN 3 10 N 4 100 N

3 LT LT and L 4 L LT and T 5 If the dimensions of a physical quantity given by ML T then the physical quantity be 1 Force if a 0 b 1 c 2 2 Pressure if a 1 b 1 c 2 3 Velocity if a 1 b 0 c 1 4 Acceleration if a 1 b 1 c 2

Which of the following units denotes the dimensions LT 27 1 Force 2 Velocity 3 Gravitational constant 4 Aceleration due to gravity

0 The SI unit of length is the meter Suppose adopt new unit of length which equals to meters The area Im expressed in terms the new unit has a magnitude 1 X 2 x2 3

Q No 27 Which of the following gives an idea about the ability of the equipment to detect small variation in the input signal quantity being measured A Readability B Accuracy C Sensitivity D Precision

The velocity v of a particle at time t is given by b where a b and c are constants t c The dimensions of a b and c are respectively AIPMT Prelims 2006 v at 1 LT 2 L and T 2 L T and LT 3 LT2 LT and L LAN 1 ITI T21