Tag: forces - vectors and moments

Questions Related to forces - vectors and moments

A body weighs 250 N on the surface of the earth. How much will it weigh half way down to the centre of the earth.?

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. 125 N

  2. 150 N

  3. 175 N

  4. 250 N.

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Correct Option: A
Explanation:

Let m be mass of a body.
$\therefore$ Weight of the body on the surface of the earth is W=mg=250N
Acceleration due to gravity at a depth d below the surface of the earth is $g^{\prime}=g\left(1-\dfrac{d}{R _{E}}\right)$
Weight of the body at depth d is
$W^{\prime}=mg^{\prime}=mg\left(1-\dfrac{d}{R _{E}}\right)$
Here, $d=\dfrac{R _{E}}{2}$
$\therefore W^{\prime}=mg\left(1-\dfrac{{R _{E}}/{2}}{R _{E}}\right)=\dfrac{mg}{2}=\dfrac{W}{2}=\dfrac{250N}{2}=125N$

Two planets have radii $r _1$ and $r _2$ and their densities are $\rho _1$ and $\rho _2$, respectively. The ratio of acceleration due to gravity on them will be.

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. $r _1\rho _1:r _2\rho _2$

  2. $r _1\rho^2 _1:r _2\rho^2 _2$

  3. $r^2 _1\rho _1:r^2 _2\rho _2$

  4. $r _1\rho _2:r _2\rho _1$

Show answer
Correct Option: A
Explanation:
$\dfrac { { g } _{ 1 } }{ { g } _{ 2 } } =\dfrac { { GM } _{ 1 } }{ { r } _{ 1 }^{ 2 } } \div \dfrac { { GM } _{ 2 } }{ { r } _{ 2 }^{ 2 } } $
$=\dfrac { { Gp } _{ 1 }\dfrac { 4 }{ 3 } \pi { r } _{ 1 }^{ 3 } }{ { r } _{ 1 }^{ 2 } } \div \dfrac { { Gp } _{ 2 }\dfrac { 4 }{ 3 } \pi { r } _{ 2 }^{ 3 } }{ { r } _{ 2 }^{ 2 } } $
$=\dfrac { { p } _{ 1 }{ r } _{ 1 } }{ { p } _{ 2 }{ r } _{ 2 } } $
$=\dfrac { { r } _{ 1 }{ p } _{ 1 } }{ { r } _{ 2 }{ p } _{ 2 } } $
$={ r } _{ 1 }{ p } _{ 1 }:{ r } _{ 2 }{ p } _{ 2 }$

An object after deforming 

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. may have different centre of mass.

  2. have same centre  of mass

  3. doesn't change its centre of gravity 

  4. none of the above 

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Correct Option: A
Explanation:

Centre of mass is a point on a physical body which behaves as if the whole mass is concentrated over there. Whenever a force acts on a body it appears to be acting on the centre of mass. 

The centre of mass depends upon how the particles of the body are scattered around it. It is closer towards the heavier regions of the body as compared to the lighter regions.  Whenever an object is deformed, its heavier regions may change their locations. As a result, the centre of mass may change its location

Racing car can corner rapidly without turning due to

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. having high centre of gravity

  2. having lower centre of gravity

  3. equal mass distribution of the car

  4. none of the above

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Correct Option: B
Explanation:

Racing car can corner rapidly without turning due to low centre of gravity. The lower the centre of gravity is more stable is the object The higher it is more likely  the object is to topple over if it is pushed.Racing cars have really low centre of gravity so that they can corner rapidly withoit turning.

Distance covered by a freely falling body in 5 seconds is

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. 85 mts

  2. 44 mts

  3. 125 mts

  4. 10 mts

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Correct Option: C

A man can jump 1.5m high on the earth. Calculate the approximate height he might be able to jump on a planet whose density is one-quarter that of the earth and whose radius is one-third of the earth's radius.

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. $1.5\ m$

  2. $15\ m$

  3. $18\ m$

  4. $28\ m$

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Correct Option: C

Which among the following is the major cause of nutation in Earth's axis:

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. Earth's Oblate spheroid shape

  2. The difference between Land and Sea hemispheres

  3. Oceanic Currents

  4. TIdal Forces

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Correct Option: D
Explanation:
In case of earth the principal sources of tidal forces are the sun and moon while continuously change location relative to each other and cause nutation in earth's axis, So option (D) correct.

The mean radius of the earth is $R$, its angular speed about its own axis $\omega$ and the acceleration due to gravity at the earth surface is $g$. The cube of radius of orbit of 'geostationary satellite' will be

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. $(R^{2}g/ \omega)$

  2. $(R^{2}\omega/ g)$

  3. $(Rg/ \omega^{2})$

  4. $(R^{2}g/ \omega^{2})$

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Correct Option: D
Explanation:

$mr\omega^{2} = \dfrac {GMm}{r^{2}}$
$\Rightarrow r\omega^{2} = \dfrac {GM}{r^{2}}$
$\Rightarrow r^{3} = \dfrac {GM}{\omega^{2}} = \dfrac {GM}{R^{2}} . \dfrac {R^{2}}{\omega^{2}}$
$\Rightarrow r^{3} = g \dfrac {R^{2}}{\omega^{2}}$
Hence (D) is correct.

Instrument used for determining specific gravity is

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. Hydrometer

  2. Barometer

  3. Calorimeter

  4. None of these

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Correct Option: A

For a ball falling in a iiquid with constant velocity, ratio of resistance force due to the liquid to that due to gravity is 

physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

  1. $\frac{{2{a^2}\rho g}}{{9xv}}$

  2. $\dfrac { 2 a ^ { 2 } \rho g } { 9 \eta ^ { 2 } }$

  3. $\dfrac { 2 a ^ { 2 } ( \rho - \sigma ) g } { 9 \eta }$

  4. none of these

Show answer
Correct Option: A
Explanation:

Force due to liquid (stokes law):

$f = 6\pi xrv$
Force due to gravity:
$\begin{array}{l} f=mg \ =\rho .\dfrac { { 4\pi { r^{ 3 } } } }{ 3 } .g \end{array}$
Ratio =
$\ \begin{array}{l} \dfrac { { 4\rho .\pi { r^{ 2 } }.g } }{ { 3.6\pi xr.v } }  \ =\dfrac { { 2{ a^{ 2 } }\rho g } }{ { 9xv } }  \end{array}$
$\therefore \,\,\,\,\,\dfrac{{2{a^2}\rho g}}{{9xv}}$
so,
Option $A$ is correct answer.