The dimensions of energy per unit volume are the same as those of _____.

1

(a)

pressure

(b)

force

(c)

modulus of elasticity

(d)

all the above

The SI units of the universal gravitational constant G are _____.

1

(a)

kg m² S^-2

(b)

kg^-l m³ S^-2

(c)

Nm² kg^-2

(d)

N kg²m^-2

The density of a cube is measured by measuring its mass and the length of its sides. If the maximum errors in the measurement of mass and length are 3% and 2% respectively, then the maximum error in the measurement of density is _____.

1

(a)

9%

(b)

9%

(c)

9%

(d)

9%

The velocity of a body moving in viscous medium is given by v =\(\frac { A }{ B } \left[ 1-{ e }^{ \frac { -t }{ b } } \right] \)where t is time, A and B are constants .Then the dimensions ot A are _____.

1

(a)

M⁰L⁰T⁰

(b)

M⁰L¹T⁰

(c)

M⁰L¹T^-2

(d)

M¹L¹T^-1

The dimensions of entropy are _____.

1

(a)

M⁰L^-1T⁰K

(b)

M⁰L^-2T⁰K²

(c)

MLT^-2K

(d)

ML²T^-2K^-1

Is it possible to have length and velocity both as fundamental quantities? Why?

1

(a)

No, since length is fundamental quantity and velocity is the derived quantity.

How many astronomical units make one metre?

1

(a)

1 m = 6.67 x 10^-12 AU

How many light years make 1 par sec?

1

(a)

3.26 light years make 1 par sec

Which of these is largest : astronomical unit, light year and par sec?

1

(a)

Par sec is larger than light year which in turn is larger than an astronomical unit.

Which unit is used to measure size of a nucleus?

1

(a)

The size of nucleus is measured in fermi
1 fermi = 10^-15 m

If \(x=a+bt+ct^{ 2 }\), where x is in meters and t is second, what is the dimensional formula of c?

1

(a)

Here, \(x=[L]\)
\(\\ t=[T];\quad x=ct^{ 2 }\)
\(\\ [L]=c\times [T^{ 2 }]\)
\(\Rightarrow \)     \(\frac { [L] }{ { [T }^{ 2 }] } =c\Rightarrow c=[LT^{ -2 }]\) 

What are the dimensions of a and b in the relation : F = a + bx, where F is force and (x) is distance?

1

(a)

\([a]=[F]=[MLT^{ -2 }]\)
\(\\ [b]=\left[ \frac { F }{ x } \right] =\left[ \frac { MLT^{ -2 } }{ L } \right] =[{ MT }^{ -2 }]\) 

How many protons would make 1kg? (Mass of proton = \(1.67\times { 10 }^{ -27 }\) kg)

1

(a)

\(5.99\times { 10 }^{ 26 }\)

Wavelength of a laser light is 6463 \(\overset { 0 }{ A } \) . Express it in nm and micron.

1

(a)

\(646.3\ nm,0.6463\mu \)

Find the value of 1 J of energy in CGS system of units.

1

(a)

10⁷ CGS units.