Free Printable Units & Dimensions Quiz 1

1.

$F=G\ \frac{m_1m_2}{r^2}$

In the given equation, G is the Universal Constant of Gravitation, F is the force acting on the 2 bodies, $m_1$ is the mass of the first object, $m_2$ is the mass of the second object and r is the distance of separation between them. What is the relation between the SI Unit and the CGS Unit of G?

a)

$SI\ Unit\ =\ 10^3\ CGS\ Unit$

b)

$SI\ Unit\ =\ 10^{-3}\ CGS\ Unit$

c)

$SI\ Unit\ =\ 10^6\ CGS\ Unit$

d)

$SI\ Unit\ =\ 10^{-6}\ CGS\ Unit$

2.

What is the ratio between the SI unit & the CGS unit of $\frac{G}{g}$ ?

a)

10

b)

0.1

c)

100

d)

1000

3.

Which of the following are units of Universal Constant of Gravitation?

a)

$kg^{-1}\ m^3\ s^{-2}$

b)

$kg^0\ m^1\ s^{-2}$

c)

$N\ m^2\ kg^{-2}$

d)

$N\ kg^{-1}$

4.

If Electrical Resistance = $\frac{Potential\ Difference}{Electric\ Current}$ ,Electrical Conductance = $\frac{Power}{\left(Potential\ Difference\right)^2}$ , V=IR and Power x Time = Energy then what is the unit of Electrical Conductance x Electrical Resistance?

a)

$J\ A^{-1}\ s^{-1}$

b)

No unit exists

c)

$J^{-1}\ A\ s$

d)

$kg^{-1}\ m^3\ s^{-2}$

5.

If angular velocity is $\frac{angular\ displacement}{time}$ , then what are the dimensions of angular acceleration?

a)

$\left[M\ ^0L^1\ T^{-2}\right]$

b)

$\left[rad\ L^1\ T^{-2}\right]$

c)

$\left[M\ ^0L^0\ T^{-2}\right]$

d)

$\left[rad\ L^0\ T^{-2}\right]$

6.

What are the dimensions of the θ $\sin\ \theta$ and μ in $e^{-\alpha t^μ}$ ?

a)

Dimensionless, Dimensionless

b)

$\left[rad\ M^0L^0T^0\right]$ , $\left[M^1L^1T^1\right]$

c)

Dimensionless, $\left[M^1L^1T^1\right]$

d)

$\left[rad\ M^0L^0T^0\right]$ , Dimensionless

7.

According to Poiseuille's Equation, $Q\ =\frac{\pi\Pr^4}{8\eta l}$ . If the percentages of error for P,r,η and l are 3%, 4% ,1% & 5% respectively, what is the total percentage error?

a)

13%

b)

25%

c)

20%

d)

1%

8.

The length of a side of a cube was measured to be (5.0±0.1)cm. What is the percentage error in the measurement of the volume of the cube?

a)

6%

b)

0.6%

c)

2%

d)

0.2%

9.

What is the rounded-off value of $\left(1.2\right)^3\times10^3$ ?

a)

$1.7\ \times10^3$

b)

$1.4\times10^3$

c)

$2.6\times10^3$

d)

$1.3\times10^3$

10.

What is the value of $\left(1.4\right)^3\times10^3$ if the cube of 1.4 is rounded off?

a)

2744

b)

2740

c)

2700

d)

1960

11.

Let the order of magnitude in $22596\times10^3$ be x.

Let the number of significant figures in 9.0516040370 be y.

Let the rounded value of $1.597\times7.2$ be z.

What is the value of $x\times y\times z$ ?

a)

343

b)

770

c)

336

d)

70

12.

It is known that the periodic time T depends only on the mass m of the body, and the stiffness c of the spring (i.e. the force per unit of linear displacement). Establish the relationship between T, m and c, given that k = 2 π.

a)

$T=2\pi\ m^2c^2$

b)

$T=2\pi\sqrt{\frac{c}{m}}$

c)

$T=2\pi\sqrt{mc}$

d)

$T=2\pi\sqrt{\frac{m}{c}}$

13.

If $A=vb+\frac{c}{t}+d^2$ , then which of the following options is correct?

a)

$d=\left[M^0L^{\frac{1}{2}}T^{-1}\right]\$

b)

$b=\left[M^0L^0T^1\right]$

c)

$c=\left[M^0L^1T^{-3}\right]\$

d)

$c=\left[M^0L^1T^{-1}\right]\$

e)

$d=\left[M^0L^1T^{-2}\right]\$

14.

Find the conversion factor between SI unit & CGS unit of energy. The order of magnitude of the obtained answer is x. Now, in $2x^2+xy+3=0$ the roots(values) of y obtained are a and b. What is the value of x + a + b?

a)

14

b)

$2\ \frac{1}{2}$

c)

$7\frac{1}{2}$

d)

0

15.

If Length, Force and Time are taken as fundamental quantities, then what are the dimensions of momentum?

a)

$\left[L^1F^0T^{-1}\right]\$

b)

$\left[L^0F^1T^1\right]\$

c)

$\left[L^0F^1T^{-1}\right]\$

d)

$\left[LFT\right]$

16.

The mass of an object was measured multiple times. The measurements obtained were 10.4 g, 11g & 11.6g. What was the percentage error in the measurements?

a)

$0.0\overline{36}$ %

b)

$0.0\overline{4}$ %

c)

$3.\overline{63}$ %

d)

$4.\overline{4}$ %

17.

The radius of a sphere was measured multiple times. The measurements obtained were 5cm, 4.99cm, 5.005cm, 4.995cm and 5.01cm. If these values were used to calculate the value of the volume of the sphere, then what was the percentage error in the measurement of the volume of the sphere?

a)

1.2%

b)

0.4%

c)

12%

d)

4%

18.

If the intensity of a wave is given by $Intensity=\frac{Power}{Area}$ (power is the rate of work done), then what are the dimensions of intensity?

a)

$\left[M^1L^0T^{-2}\right]\$

b)

$\left[M^1L^2T^{-3}\right]$

c)

$\left[M^1L^0T^{-3}\right]\$

d)

$\left[M^1L^4T^{-3}\right]$

19.

If U is potential energy, G is the universal constant of gravitation, M is the mass of the bigger object, m is the mass of the smaller object and r is the distance of separation between the 2 objects, find the relation between U, G, M, m and r while taking U as the reference?

a)

$U=\frac{GMm}{r^2}$

b)

$U=-\frac{GMm}{r}$

c)

$U=\frac{GM}{r^2}$

d)

$u=G\ M\ m\ r^2$

20.

If g is the acceleration due to gravity, M is the mass of the bigger object (object causing acceleration due to gravity) and r is the distance between the objects, establish the relationship between the given quantities while taking g as the quantity of reference.

a)

$g=\frac{GM}{r^2}$

b)

$g=\frac{GM}{r}$

c)

$g=GMr$

d)

$g=\frac{Mr}{G}$

21.

If the number of significant figures in 1.785001894000 is a, the order of magnitude of $299792458\times10^{-2}$ is b and the rounded-off value of $1.518\times2.1$ is c, then what is the value of $\frac{a+b}{c}$ ?

(a)

22.

What is the order of magnitude of the conversion factor of the SI unit and the CGS unit of acceleration due to gravity?

(a)

23.

If energy (E), mass (M) and power(P) are taken as fundamental quantities, the dimensions of velocity are obtained as $\left[E^xM^yP^z\right]$ . What is the value of x + y + z?

(a)

24.

The length of a side of a cube was measured to be $10.0\pm0.5$ cm. What is the percentage error in the measurement of its area?

(a)

25.

The length, breadth and height of a room were measured to be $2.5\pm0.1m$ , $2\pm0.7m$ & $4.00\pm0.1m$ . What was the percentage error in the measurement of its volume?

(a)

Units & Dimensions Quiz 1

Total questions: 25

Worksheet time: 45mins

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