Tag: measurement of area, volume and density

Questions Related to measurement of area, volume and density

 In a given system of units, the ratio of unit of volume to that of its area gives 

  1. Density

  2. Length

  3. Mass

  4. Decibel


Correct Option: B
Explanation:

SI Unit of volume is $m^3$ 

Unit of area is $m^2$
So $\dfrac{Volume}{area}=m^3/m^2=m$, that's the unit of length 

A cubic metre of water at $0^o$C is solidified into ice, density of ice is $0.96$ of water at $0^o$C. Which of the following deductions are true?
$1$. Water expands when solidified.
$2$. Ice will float in water at $0^o$C with half its volume above the surface.
$3$. Density of all liquids are higher than its density when solidified.

  1. $3$ only

  2. $2$ only

  3. $1$ only

  4. $1$ and $2$


Correct Option: C

A cubical block of wood of specific gravity $0.5$ and a chunk of concrete of specific gravity $2.5$ are fastened together. The ratio of mass of wood to the mass of concert which makes the combination to float with its entire volume submerged in water is 

  1. $1/5$

  2. $1/3$

  3. $3/5$

  4. $2/5$


Correct Option: A

There are $n\ sets$ of real numbers. In every set there are four real numbers in AP. Such that the square of the last term is equal to the sum of the square of the first three terms. Then: -

  1. $N = 4$

  2. $N = 1000$

  3. $N = 10$

  4. $N \rightarrow \infty$


Correct Option: C

Four  positive charges $ ( 2 \sqrt 2-1 )Q $ are arranged at corner of square . another charge q is placed at the centre of the square. resultant force acting on each corner is zero if q is :

  1. $-7Q/4$

  2. $-4Q/ 7$

  3. $-Q$

  4. $none$


Correct Option: C

A public park, in the form of a square, has an area of $(100 \pm 0.2 )m^2 $ .The side of park is :

  1. $ (10 \pm 0.01 ) m $

  2. $ (10 \pm 0.1 ) m $

  3. $ (10 \pm 0.02 ) m $

  4. $ (10 \pm 0.2 ) m $


Correct Option: A
Explanation:

Let the side length of the square park is $l$.

The area of a square is given as,

$A = {l^2}$

$100 = {l^2}$

$l = 10\;{\rm{m}}$

The error in length is given as,

$\dfrac{{\Delta A}}{A} = 2\dfrac{{\Delta l}}{l}$

$\dfrac{{0.2}}{{100}} = 2\dfrac{{\Delta l}}{{10}}$

$\Delta l = 0.01\;{\rm{m}}$

Thus, the side of the park is $\left( {10 \pm 0.01} \right)\;{\rm{m}}$.

The mass of 0.5 litre of hydrogen gas at NTP will be approximately

  1. 0.0892 g

  2. 0.045 g

  3. 2 g

  4. 22.4 g


Correct Option: B
Explanation:

$PV=mRT$

Under NTP 
 $P=10^5N/m,\ V=0.5L=0.5\times10^{-3},\ T=298K,\ R=8300/2$

$\Rightarrow 10^5\times 0.5\times 10^{-2}=m\times 8300\times 298/2$
$\Rightarrow m=0.042\ g$

The space occupied by the object is called ....................... .

  1. Area

  2. Mass

  3. density

  4. Volume


Correct Option: D
Explanation:

Volume of the object is defined as the space occupied by the object.

Mass per unit volume is ....................... .

  1. Density

  2. Mass

  3. Volume

  4. All of the above


Correct Option: A
Explanation:
Density of object is defined as the mass of the body per unit is volume.
$Density = \dfrac{Mass}{Volume}$

Express $1  ml $ in $m^3$.

  1. $10^{-3}$

  2. $10^{-6}$

  3. $10^{-9}$

  4. None of the above


Correct Option: B
Explanation:

$1ml=10^{-3}L=10^{-3}\times10^{-3}m^3=10^{-6}m^3$