units and measurements class 11 numericals pdf

                 Dear students numericals of units and measurements class 11 numericals pdf neet questions and units and measurements jee questions aiims important questions have been collected at one place to get you all prepared for your neetaiims ,jee main, advance exams as well as cbse board exams and other board exams. Visit my nawendu classes youtube channel for more help.


1.(a)The volume of a cube of side1 cm is equal to …….. ${{m}^{3}}$ .

   (b)The surface area of a solid cylinder of radius 2cm and height 10 cm is equal to ……..${{\left( mm \right)}^{2}}$ .

    (c) A vehicle moving with a speed of 18 km/h covers ………..m in 1 second.

    (d) G = 6.67x ${{10}^{-11}}$ N${{m}^{2}}{{\left( kg \right)}^{-2}}$=……………${{\left( cm \right)}^{3}}{{s}^{-2}}{{g}^{-1}}$

Answer- (a)${{10}^{-6}}$ (b)1.5x ${{10}^{4}}$   (c) 5   (d) 6.67x${{10}^{-8}}$  

2. Suppose the acceleration due to gravity at a place is 10m/${{s}^{2}}$ .Find its value in $cm/{{\left( \min ute \right)}^{2}}$ .

Answer- 36x ${{10}^{5}}cm/{{\left( \min ute \right)}^{2}}$

3.  The average speed of a snail is 0.020miles/hour and that of a leopard is 70 miles/hour.                     Convert these speed in SI units.

Answer- 0.0089m/s , 31 m/s

4. The surface tension of water is 72 dyne/cm.Convert it in SI unit.

Answer- 0.072 N/m

5. The density of material in cgs system of unit is 4$g/c{{m}^{3}}$. In a system of units in which unit of length is 10 cm and unit of mass is 100g.The value of density of material will be

    CBSE PMT 2011

Answer-  40 unit

6. In a particular system the unit of length mass and time are chosen to be 10cm, 10 g and

         0.1s respectively .The unit of force in this system will be equivalent to

   CBSE PMT 1997

 Answer.- 0.1N

7.Parsec is the unit of 

   AIIMS 2005

  Answer-   Distance

  8. Write the dimensional formula of the followings.

a. Inductance Karnataka cet 2003

b. Permittivity jee main 2013

c. Magnetic flux IIT 1982

d. Planks Constant  IIT 1985

e. Capacitance IIT 1983, MP PMT 1979

f. Universal gravitational constant

AIIMS 2002 ,AFMC 1999 ,BCECE 2003

g. Potential energy MP PET 2003

h. R/L MP PET 2003

i. L /RCV ROORKEE 1994

j. Impulse CBSE PMT 1991 ,BCECE 2003

             Where R-resistance ,L- inductance , C- capacitance , V- potential difference

 Answer- a. ${{M}^{1}}{{L}^{2}}{{T}^{-2}}{{A}^{-2}}$

             b. ${{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}$  

             c. ${{M}^{1}}{{L}^{2}}{{T}^{-1}}{{A}^{-1}}$  

             d. ${{M}^{1}}{{L}^{2}}{{T}^{-1}}$  

             e. ${{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}$  

             f. ${{M}^{-1}}{{L}^{4}}{{T}^{-2}}$  

             g. ${{M}^{1}}{{L}^{2}}{{T}^{-2}}$  

              h. ${{T}^{1}}$  

              i.  ${{A}^{-1}}{{T}^{6}}$      

              j. ${{M}^{1}}{{L}^{2}}{{T}^{-1}}$

 9. What is the dimensions of impedance ?


   Answer-  $M{{L}^{2}}{{T}^{-3}}{{A}^{-2}}$

10.  Dimension of coefficient of viscosity is

   Answer-  $M{{L}^{-1}}{{T}^{-1}}$

11. What is the dimensional formula for gravitational constant ?

         AIIMS 2000

Answer- ${{M}^{-1}}{{L}^{3}}{{T}^{-2}}$

12.  Using mass (M), length (L), and time (T) and current (A) as fundamental quantities. The

           dimensions of permeability are 


Answer- $ML{{A}^{-2}}{{T}^{-2}}$

 13. The dimensional formula of the constant a and b in wander waals equation

        ( P+$\frac{a}{{{V}^{2}}}$) (V-b)=RT, 

Where P=pressure,V=volume,R=gas constant and T=teperature

Answer- $M{{L}^{5}}{{T}^{-2}}$,${{L}^{3}}$

14.The displacement of a particle moving along X-axis with respect to time is x=at+b${{t}^{2}}$-c${{t}^{3}}$.

         The dimensions of a b and c are

 Answer-  L ${{T}^{-1}}$ L ${{T}^{-2}}$ , L ${{T}^{-3}}$

15.   The velocity of a particle is given by v= at + b/ t+c where t is time. Dimensions of a ,b and c are? 


Answer- $L{{T}^{-2}}$, L and T

16. Force on a particle in one dimensional motion is given by $F=Av+Bt+\frac{Cx}{At+D}$,Where F= force,V= speed ,t = time ,x = position and  A, B, C, D are constants. Dimension of C will be.

Answer - ${{M}^{2}}{{L}^{0}}{{T}^{-2}}$ 

17. Which of the following physical quantities do not have same dimensions?

            a. Pressure and stress

            b. Tension and surface tension

            c.  Strain and angle

            d.  Energy and work

        AIIMS 2007

Answer-  b. tension and surface tension

18. The force F on a sphere of   radius r moving in a medium with velocity v is given by F =

          6 π $\eta $ rv. The dimensions of $\eta $  are

       CBSE PMT 1997

Answer- \[M{{L}^{-1}}{{T}^{-1}}\]

19. The ratio of the dimension of plank’s constant and that of the moment of inertia is the dimension of

   AIIMS- 2010 

Answer- Angular momentum

20. If C and R denote capacitance and resistance respectively , then the dimensional formula of CR is 


Answer- ${{M}^{0}}{{L}^{0}}T$

21. The force F is given by expression F = A cos(Bx) + C sin(Dt), where x is the displacement and t is the time. Then, dimension of D/B is same as that of 

     AIIMS- 2013 

Answer- Velocity [$L{{T}^{-1}}$] 

22. The dimensional formula of product and quotient of two physical quantities A and B are given by

  $\left[ AB \right]=\left[ M{{L}^{2}}{{T}^{-2}} \right]$ ;$\left[ \frac{A}{B} \right]=\left[ M{{T}^{-2}} \right]$ . The quantities A and B respectively are.

Answer- force and displacement

23. If energy E,velocity V and timeT are choosen as the fundamental quantities,the dimensional formula of surface tension will be    

      CBSE AIPMT 2015

 Answer- $E{{V}^{-2}}{{T}^{-2}}$

24. The speed of light ( c) gravitational constant (G) and planks constant (h) are taken as

              Fundamental units in a system. The dimension of time in the new system should be

           AIIMS- 2008 

     Answer- ${{G}^{1/2}}{{h}^{1/2}}{{c}^{-5/2}}$

25. If force F ,velocity V and time T are taken as fundamental units, then the dimensions of mass are

    CBSE AIPMT 2014

Answer- $F{{V}^{-1}}T$  

26. Taking force, length and time to be the fundamental quantities .Find the dimension of

           a. Density      b. Pressure        c. Momentum      d. Energy

  Answer- a.F${{L}^{-4}}{{T}^{2}}$        b.F${{L}^{-2}}$      c.FT        d. FL

27. Test ,the following equations are dimensionally correct  or incorrect.

   a. h= 2S$\frac{\cos \theta }{\rho rg}$            b. v = $\sqrt{\frac{P}{\rho }}$

    c. V =$\frac{\pi {{\Pr }^{4}}t}{8\eta L}$          d. T = $\frac{1}{2\pi }\sqrt{\frac{mgL}{I}}$

  Where h = height ,S= surface tension ,v = velocity ,V= volume ,T = timeperiod  ,$\rho $ =  density,m= mass ,r= radius ,g= acceleration due to gravity , L= length , I= moment of inertia

   P= pressure , $\eta $= coefficient of viscosity.

Answer – a. Correct  b. Correct  c. Correct   d. Incorrect

28. Find dimensional formula

      (1) $\frac{dx}{dt}$ (2)  m$\frac{{{d}^{2}}x}{d{{t}^{2}}}$  (3)  $\int{vdt}$  (4)$\int{adt}$

  Where x= displacement, t= time, v= velocity  ,a =acceleration ,m= mass

 Answer- (1)  ${{M}^{0}}{{L}^{1}}{{T}^{-1}}$   (2) ${{M}^{1}}{{L}^{1}}{{T}^{-2}}$                 

                (3)  ${{M}^{0}}{{L}^{1}}{{T}^{0}}$   (4) ${{M}^{0}}{{L}^{1}}{{T}^{-1}}$  

 29. If $\int{\frac{dx}{\sqrt{2ax-{{x}^{2}}}}}={{a}^{n}}{{\sin }^{-1}}\left[ \frac{x}{a}-1 \right]$ ;then the value of n is

Answer -  0

30. Let x and a stand for distance. Is $\int{\frac{dx}{\sqrt{{{a}^{2}}-{{x}^{2}}}}}=\frac{1}{a}{{\sin }^{-1}}\frac{a}{x}$  dimensionally correct ?

Answer- No

31. Consider the equation  $\frac{d}{dt}\left( \int{\overset{\to }{\mathop{F}}\,\cdot \overset{\to }{\mathop{ds}}\,} \right)=A\left( \overset{\to }{\mathop{F}}\,\cdot \overset{\to }{\mathop{P}}\, \right)$

  Where F = Force, s =displacement ,t = time, and p = momentum .The dimensional formula of A will be.

 Answer-   ${{M}^{-1}}{{L}^{0}}{{T}^{0}}$

32. If dimensions of critical velocity \[{{V}_{C}}\] of a liquid flowing through a tube are expressed as [${{\eta }^{x}}{{\rho }^{y}}{{r}^{z}}$ ], where $\eta ,\rho $  and r are the coefficient of Viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by


Answer-  1,-1,-1

33.The frequency of vibration of a string depends on the length L between the nodes, the tension F in the string and its mass per unit length m. Guess the expression for its frequency from dimensional analysis.

Answer- \[\frac{k}{L}\sqrt{\frac{F}{m}}\]

34. If the time period(T) of vibration of a liquid drop depends on surface tension (s), radius(r) of the drop and density (ῥ) of the liquid, then the expression of T is 

       AIIMS- 2007 

 Answer-  $T=k\sqrt{\rho {{r}^{3}}/{{s}^{1/2}}}$  

35. The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to \[{{\left( pressure\text{ }difference\text{ }across\text{ }the\text{ }ends \right)}^{n}}\]and ${{\left( average\text{ }velocity \right)}^{m}}$of the liquid. Which of the following relation is correct? 

      AIIMS- 2005 

Answer-  ${{m}^{2}}=n$  

36.The dimensions of $\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}$ , where ${{\varepsilon }_{0}}$   is permittivity of free space and E is electric field, are 

       CBSE AIPMT 2010 

 Answer- $M{{L}^{-1}}{{T}^{-2}}$

37.The dimensions of  ${{\left( {{\mu }_{0}}{{\varepsilon }_{0}} \right)}^{-1/2}}$

${{\mu }_{0}}$ -Permeability of air and ${{\varepsilon }_{0}}$ -permittivity of air

  CBSE AIPM T 2012 

Answer- $L{{T}^{-1}}$

38. A physical quantity of the dimensions of length that can be formed out c ,G ,$\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}}$  is 

 Where c-velocity of light ,G-universal constant of gravitation ,e-charge

    NEET 2017

Answer-  a

39. IF \[\alpha =\frac{F}{{{V}^{2}}}\sin \beta t\] ,find dimensions of $\alpha $ and $\beta $ .Here v = velocity ,F = force and t = time.

 Answer- $\left[ \beta  \right]=\left[ {{T}^{-1}} \right]$ , $\left[ \alpha  \right]=\left[ M{{L}^{-1}} \right]$

40. In the formula X = 5Y${{Z}^{2}}$ , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

   IIT 2019 Main, 10 April II 

Answer-  ${{M}^{-3}}{{L}^{-2}}{{T}^{8}}{{A}^{4}}$

41.Let I, r, c, and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of  $\frac{l}{rcv}$ in SI units will be 

  IIT 2019 Main, 12 Jan I 

Answer-  ${{A}^{-1}}$

42. In the relation,p= $\frac{\alpha }{\beta }{{e}^{\frac{-\alpha z}{k\theta }}}$

 p is pressure, Z is distance, k is Boltzmann’s constant and  $\theta $ is the temperature. The dimensional formula of $\beta $  will be      

  IIT 2004, 2M 

 Answer-  ${{M}^{^{0}}}{{L}^{2}}{{T}^{0}}$

43.The force of interaction between two atoms is given by F=$\alpha \beta \exp \left( -\frac{{{x}^{2}}}{\alpha KT} \right)$ ; where x is distance, k is the Boltzmann constant and T is temperature and $\alpha and\beta $  are two constants. The dimensions of $\beta $ is

  IIT 2019 Main, 11 Jan I

Answer-  ${{M}^{2}}L{{T}^{-4}}$

44.1f surface tension (S), moment of inertia (l) and Planck’s constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be 

   IIT 2019 Main, 8 April II  


45. Which of the following combinations has the dimension of electrical resistance (${{\varepsilon }_{0}}$is the permittivity of vacuum and ${{\mu }_{0}}$ is the permeability of vacuum)? 

  IIT 2019 Main; 12 April II 


No comments

Theme images by belknap. Powered by Blogger.