Tag: turning effects of forces

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Questions Related to turning effects of forces

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.

Multiple choice physics motion of system of particles and rigid bodies centre of gravity turning effects of forces forces - vectors and moments

What is the position of centre of gravity of a cylinder?

  1. At the center of base circle

  2. At the center of top circle

  3. Cannot be determined

  4. At the mid point on the axis of cylinder
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Centre of gravity means a point from which the weight of a body or system may be considered to act. In uniform gravity it is the same as the centre of mass. For regular shaped bodies it lies at the centre of the that particular body. Hence for a cylinder centre of gravity lies at the midpoint of the axis of the cylinder.

Multiple choice physics motion of system of particles and rigid bodies centre of gravity turning effects of forces forces - vectors and moments

In an artificial satellite, the use of a pendulum watch is discarded, because :

  1. The satellite is in a constant state of motion

  2. The effective value of $g$ becomes zero in the artificial satellite

  3. The periodic time of the pendulum watch is reduced

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A pendulum watch relies on gravity to oscillate. Inside an orbiting satellite, objects are in a state of free fall, meaning the effective gravitational acceleration (g) is zero, causing the pendulum to stop oscillating.

Multiple choice physics motion of system of particles and rigid bodies centre of gravity turning effects of forces forces - vectors and moments

Given that there is a relationship between the orbital radius of a planet and its period of revolution and that the periods of revolution of Mercury, Earth, Jupiter and Neptune and nearly 0.24, 1, 11.8 and 165 years. It follows that the period of revolution of
1. Venus is less than 0.24 years
2. Mars is less than 12 years
3. Uranus is more than 165 years
4. Uranus is less than 165 years but more than 12 years.

  1. 1 and 3

  2. 4 only

  3. 3 o nly

  4. 2 and 4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Kepler's third law states that the square of the orbital period is proportional to the cube of the semi-major axis (distance from the Sun). Therefore, planets further from the Sun have longer orbital periods. Mars (between Earth and Jupiter) must have a period between 1 and 11.8 years. Uranus (further than Neptune) would have a period longer than 165 years. The logic in option 2 and 4 fits the observed orbital distances.