Tag: centre of gravity

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Questions Related to centre of gravity

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

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

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

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

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

  4. $(R^{2}g/ \omega^{2})$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

If a charge particle projected in a gravity-free room it does not deflect, 

  1. electric field and magnetic field must be zero

  2. both electric field and magnetic field may be present

  3. electric field will be zero and magnetic field may be zero

  4. electric field may be zero and magnetic field may be zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a charged particle moves through a region without deflection, the net force must be zero. The Lorentz force is F = q(E + v x B). If E = 0 and B = 0, the force is zero. While other configurations exist (like E and B being parallel to v), the most fundamental condition for no deflection regardless of velocity is that both fields are zero.

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

If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take:

  1. 96 h

  2. 48 h

  3. 6 h

  4. 1.5 h
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know that angular momentum of spin $\displaystyle =I\omega $
Bythe conservation of angular momentum
$\displaystyle \frac { 2 }{ 5 } M{ R }^{ 2 }.\frac { 2\pi  }{ T } =\frac { 2 }{ 5 } M{ \left( \frac { R }{ 4 }  \right)  }^{ 2 }.\frac { 2\pi  }{ T' } $
$\displaystyle T'=\frac { T }{ 16 } =\frac { 24 }{ 16 } =1.5h$

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

Weight $W _ { m }$ of the body can be given as 

  1. $m g - m \frac { \left( v _ { e } + v \right) ^ { 2 } } { R }$

  2. $m g - m \frac { \left( v _ { e } - v \right) ^ { 2 } } { R }$

  3. $\frac { m } { R } \left[ v _ { e } ^ { 2 } - \left( v _ { e } + v \right) ^ { 2 } \right]$

  4. $m g + m \frac { \left( v _ { e } + v \right) ^ { 2 } } { R }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This relates to the effective weight of a body in a rotating frame or a non-inertial frame. The term m(v_e + v)^2 / R represents the centrifugal force component acting on the body, which reduces the effective gravitational weight.

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

Why are the passengers in the upper deck of a double-decker bus not allowed to stand?

  1. This ensures that the centre of gravity of the system may not rise up and the bus may not be toppled due to unstable equilibrium

  2. This ensures smaller centripetal force, thus helping the driver to negotiate the roundabouts properly

  3. If the passengers are in standing position, they may start oscillating due to jerks and there is a possibility of resonance, causing the bus to be toppled

  4. This is just for the safety reason
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When the passengers stand, the center of gravity rises. If it rises much it becomes unstable and may topple down.

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

Can the centre of gravity be situated outside the material of the body ?

  1. Yes

  2. No

  3. Can't say

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Yes, it can. For example, in case of a ring, it is situated at the centre of that circle. But the material is only along the circumference. Hence centre of gravity is situated outside the material of the body.