If f = X², then the relative error in f is ______________

(a)

\(2\triangle x \over x\)

(b)

\((\triangle x)^2 \over x\)

(c)

\(\triangle x \over x\)

(d)

\((\triangle x)^2\)

Rounding off value of 1.87b is _________________.

(a)

1.87

(b)

18.7

(c)

1.88

(d)

1.86

The length and breadth of a rectangle are 6.01m and 12m. Taking the significant figure into account the area of the rectangle is _______________.

(a)

72.00 m²

(b)

72.1 cm²

(c)

72 m²

(d)

72.12 m²

Which of the following digits are significant?

(a)

zero digits

(b)

zeros at the end without a decimal point

(c)

all zeros between two non-zeros digits, irrespective of the decimal point

(d)

all the above

Which one of the following is used to determine very large distance?

(a)

Radar method

(b)

Parallax method

(c)

Triangulation method

(d)

all the above

The same error repeated every time in the series of observation is known as _____________error.

(a)

random

(b)

constant

(c)

gross

(d)

systematic

Two quantities A and B have different dimensions which mathematical operation given below is physically meaningful?

(a)

A/B

(b)

A+B

(c)

A-B

(d)

A=B

The dimensional formula for relative density is ____________.

(a)

ML^-3

(b)

M^OL^-3

(c)

M^oL^oT^o

(d)

M^oL^oT^-1

The dimension of Planck's constant are same as ____________.

(a)

energy

(b)

power

(c)

angular momentum

(d)

momentum

Of the following__________________ has dimensions.

(a)

strain

(b)

angle

(c)

gravitational constant

(d)

refractive index

________________ have the same dimensional formula.

(a)

Force and momentum

(b)

Density and linear density

(c)

Lightyear and wavelength

(d)

Stress and strain

Which of the following is dimensional constant?

(a)

Refractive index

(b)

Poisson's ratio

(c)

strain

(d)

gravitational constant

The dimension of a quantity \(hy \over c\) where h is the planck's constants, \(\gamma\) is the frequency and c is the velocity of light are _______________.

(a)

MT^-1

(b)

MLT^-1

(c)

MLT^-2

(d)

ML²T²

If the energy E = G^Ph^qC^r where G is the universal gravitational constant, h is the planck's constant and C is the velocity of light, then the values of p, q and r are respectively ______________.

(a)

\(-{1\over2},{1\over2}and {5\over2}\)

(b)

\({1\over2},-{1\over2}and-{5\over2}\)

(c)

\(-{1\over2},{1\over2}and {3\over2}\)

(d)

\(-{1\over2},-{1\over2}and- {3\over2}\)

The dimensional formula of the constant "a" in Vanderwaals gas equation is \((p+{a\over v^2})(v-b)=RT\)

(a)

MT⁵T^-2

(b)

ML³T^-2

(c)

ML²T^-1

(d)

ML⁵T^-3

Force F is given by F = at + bt². Where "t" is time. What are the dimensions of "a" and "cb"?

(a)

MLT^-1and MLT^o

(b)

MLT^-3and MLT^-4

(c)

MLT^-3and MLT⁴

(d)

MLT³and MLT^-4

In an expression, four quantities a, b, c and d are measured with % error. 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows P = \({a^3b^2\over cd}\%\) error in P is _____________.

(a)

10

(b)

7

(c)

4

(d)

14

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be ______________.

(a)

Ey^-1 T²

(b)

Ey^-2 T²

(c)

Ey¹ T^-2

(d)

Ey^-2 T^-2

The force F is given interms of time t and displacement x by the equation F = A cos Bx + C sin Dt. The dimensional formula af D/B _____________.

(a)

ML⁰T⁰

(b)

ML⁰T⁰

(c)

M⁰LT^-1

(d)

M⁰L⁰T⁰

Which of the following will be the same dimension as that of time?

(a)

\(L\over R\)

(b)

\(C\over L\)

(c)

LC

(d)

\({R\over L}\)

Length can't be measured by _____________.

(a)

fermi

(b)

micron

(c)

debye

(d)

light year

The physicist who made major contributions to the generation of electromagnetic waves is ____________.

(a)

Rudolf Hertz

(b)

Michael Faraday

(c)

J. J. Thomson

(d)

Isaac Newton

Two resistors of resistances R₁ = 10 ± 0.3 ohm and R₂ = 20 ± 0.4 ohm are connected in parallel. The equivalent resistance of the parallel combination in ohm is ____________.

(a)

5.7 ± 0.1

(b)

15.2 ± 0.2

(c)

6.7 ± 0.2

(d)

9.5 ± 0.1

Ihe density of a cube is measured by measuring its mass and length of its side. If the maximum error in the measurement of mass and length are 3% and 2% respectively, the maximum error in the measurement of density is ________________.

(a)

1%

(b)

9%

(c)

7%

(d)

5%

While measuring acceleration due to gravity, by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error , of 3% in the value of time period. The percentage error in the measurement of 'g' is _______________.

(a)

2%

(b)

4%

(c)

10%

(d)

7%

The number of significant figures in 0.0006012 m is _______________.

(a)

3

(b)

4

(c)

5

(d)

7

The number of significant figures in 2.64\(\times\)10⁴ kg is ________________.

(a)

2

(b)

4

(c)

3

(d)

5

Identify the pair of physical quantities having the same dimensions.

(a)

Light year and period of a pendulum

(b)

Angular momentum and torque

(c)

Energy and Modulus of elasticity

(d)

Torque and work

L,C and R represent physical quantities inductance. capacitance and resistance respectively. The combination which has the dimensions of frequency is _______________.

(a)

\(\frac{1}{LC}\)

(b)

\(\frac{R}{L}\)

(c)

\(\frac{1}{RL}\)

(d)

\(\frac{C}{L}\)

If C is the capacitance and V is the potential, the dimensional formula for CV² is _______________.

(a)

ML²T^-2

(b)

ML^-1T^-2

(c)

ML^-2T^-3

(d)

ML²T^-1

The displacement of a particle moving afong x-axis with respect to time is given by x =at + bt² - ct³. The dimensions of b are ________________.

(a)

L⁰T^-3

(b)

LT^-3

(c)

LT^-2

(d)

LT³

The Van der Waal equation for n moles of a real gas is \((P+\frac{a}{V^2})(V-b)=RT\) where P is the pressure. V is the volume. T is the absolute temperature. R is the molar gas constant and 'a' and 'b' are Van der Waal constants. The dimensions of 'a' are the same as those of _______________.

(a)

\(\frac{P}{V}\)

(b)

PV

(c)

PV2

(d)

P2V

The dimensions of \(\frac { 1 }{ \sqrt { { \mu }_{ 0 }{ \varepsilon }_{ 0 } } } \) are the same as those of  ______________.

(a)

energy

(b)

acceleration

(c)

force

(d)

velocity

The speed of gravity waves in water is proportional to \(\lambda^a\rho^bg^y\) where \(\lambda\) is the wavelength, p is the density of water and g is the acceleration due to gravity. The correct relation between \(\alpha,\beta\) and r is _______________.

(a)

\(\alpha\ne\beta\ne\gamma\)

(b)

\(\alpha\ne\gamma=\beta\)

(c)

\(\alpha=\gamma\ne\beta\)

(d)

\(\alpha=\beta=\gamma\)

If E and B respectively, represent electric field and magnetic induction field, then the ratio \(\frac{E}{B}\) has the dimensions of _____________.

(a)

angle

(b)

acceleration

(c)

velocity

(d)

displacement

A force F is applied on to a square plate of side L. If the percentage error in determining L is 2% and that in F is 4%, the percentage error in pressure is ____________.

(a)

8%

(b)

4%

(c)

6%

(d)

3%

A physical quantity of the dimensions of length that can be formed out of c, G and \(\frac{e^2}{4\pi\varepsilon_0}\) is [c is velocity of light, G is the universal constant of gravitation and e is charge] _______________.

(a)

\(c^2[G\frac{e^2}{4\pi\varepsilon_0}]^{\frac{1}{2}}\)

(b)

\(\frac{1}{c^2}[\frac{e^2}{G4\pi\varepsilon_0}]^{\frac{1}{2}}\)

(c)

\(\frac{1}{c}G\frac{e^2}{4\pi\varepsilon_0}\)

(d)

\(\frac{1}{c^2}[G\frac{e^2}{4\pi\varepsilon_0}]^{\frac{1}{2}}\)

If dimensions of critical velocity V_c of a liquid flowing through a tube are expressed as [\(\eta^x\rho^y\gamma^z\)] where \(\eta\), \(\rho\) and \(\gamma\) are the coefficient of viscosity of liquid, density or liquid and radius of the tube respectively, then the values of x, y and z are given by ________________.

(a)

-1,-1,-1

(b)

1,1,1

(c)

1,-1,-1

(d)

-1,-1,1

The pair of quantities having same dimensions is ______________.

(a)

Impulse and Surface Tension

(b)

Angular momentum and Work

(c)

Work and Torque

(d)

Young's modulus and Energy

The damping force on an oscillator is directly proportional to the velocity, The units of the constant of proportionality are ______________.

(a)

kgms^-1

(b)

kgms^-2

(c)

kgs^-1

(d)

kgs

A student measures the distance traversed in free fall of a body, initially at rest, in a given time, He uses this data to estimate g, the acceleration due to gravity, If the maximum percentage errors in measurement of the distance and the time are e₁ and e₂ respectively, the percentage error in the estimation of g is ______________.

(a)

e₂-e₁

(b)

e₁+2e₂

(c)

e₁+e₂

(d)

e₁-2e₂

Which two of the following five physical parameters have the same dimensions?
1. energy density
2. refractive index
3. dielectric constant
4. Young's modulus
5. magnetic field

(a)

1 and 4

(b)

1 and 5

(c)

2 and 4

(d)

3 and 5

Which pair do not have equal dimensions?

(a)

Energy and torque

(b)

Force and impulse

(c)

Angular momentum and Planck constant

(d)

Elastic modulus and pressure

An equation is given here \((P+\frac{a}{V^2})=b\frac{\theta}{V}\) where P = Pressure, V = Volume and θ = Absolute temperature. If a and b are constants, the dimensions of a will be ______________.

(a)

[ML^-5T^-1]

(b)

[ML⁵T¹]

(c)

[ML⁵T^-2]

(d)

[M^-1L⁵T²]

TIle dimensions of RC is ______________.

(a)

square of time

(b)

square of inverse time

(c)

time

(d)

inverse time

Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be ____________.

(a)

8%

(b)

2%

(c)

12%

(d)

10%

Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is P. The viscosity of oil is given by \(\eta=\frac{P(r^2-x^2)}{4vl}\) where v is the velocity of oil at a distance x from the axis of the tube. The dimensions of \(\eta\) are ______________.

(a)

[M⁰L⁰T⁰]

(b)

[MLT^-1]

(c)

[ML²T^-2]

(d)

[ML^-1T^-1]

The time dependence of a Physical quantity p is given by P = P₀ exp(-at²) where a is a constant and t is the time. The constant a _____________.

(a)

is diemensionless

(b)

has dimensions[T^-2]

(c)

has dimensions[T²]

(d)

has dimensions of P

A certain body weighs 22.42 g and has a measured volume of 4.7cc. The possible error in thc measurement of mass and volume are 0.01 g and 01 cc. Then maximum error in the density will be ______________.

(a)

22%

(b)

2%

(c)

0.2%

(d)

0.02%

The dimensional formula of permeability of free space m₀ is ______________.

(a)

[MLT^-2A^-2]

(b)

[M⁰L¹T]

(c)

[M⁰L²T^-1A²]

(d)

none of these