Tag: forces - vectors and moments

Questions Related to forces - vectors and moments

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

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

  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

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Correct Option: A

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:

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

  1. 96 h

  2. 48 h

  3. 6 h

  4. 1.5 h

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Correct Option: D
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' } $
$\displaystyle T'=\frac { T }{ 16 } =\frac { 24 }{ 16 } =1.5h$

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

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

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

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Correct Option: A

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

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

  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

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Correct Option: A
Explanation:

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

Which of the following pairs of forces cannot be added to give a resultant force of $4N$?

physics forces - vectors and moments concept of force and its unit force - push or pull forces

  1. $2 N$ and $8 N$

  2. $2 N$ and $2 N$

  3. $2 N$ and $6 N$

  4. $2 N$ and $4 N$

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Correct Option: A
Explanation:

Resultant force, 

$F=\sqrt{F _1^2+F _2^2+2F _1F _2cos\theta}$. . . . . . . . .(1)
Lets consider the option A,

$F _1=2N$
$F _2=8N$

For maximum resultant force, $cos\theta=1$
From equation (1),
$F _{max}=\sqrt{F _1^2+F _2^2+2F _1F _2}=\sqrt{(F _1+F _2)^2}$
$F _{max}=F _1+F _2$
$F _{max}=8+2=10N$
For minimum resultant force, $cos\theta=-1$
$F _{min}=\sqrt{F _1^2+F _2^2-2F1F _2}=\sqrt{(F _1-F _2)^2}$
$F _{min}=\sqrt{(2-8)^2}=6N$
So, the $4N$ does not lie within this range. Thus it is not possible to have it as resultant force.
The correct option is A.

Two forces 12 N and 5 N are acting perpendicular to each other. Then the net force acting is.

physics forces - vectors and moments concept of force and its unit force - push or pull forces

  1. 17 N

  2. 18 N

  3. 7 N

  4. zero

  5. 13 N

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Correct Option: E
Explanation:

$ \vec F _{net} = \vec F _1 +\vec F _2$

$| \vec F _{net}| = \sqrt{F _1^2 +F _2^2 +2F _1F _2\cos\theta}$
$| \vec F _{net}| = \sqrt{12^2 +5^2 +2\times 12 \times 5\cos 90^0}$
$| \vec F _{net}| = \sqrt{12^2 +5^2 }$
$| \vec F _{net}| = 13N$
Therefore, E is correct option.

Two forces of $12 \mathrm { N } \text { and } 8 \mathrm { N }$ acts upon a body. The resultant force on the body has maximum value of

physics forces - vectors and moments concept of force and its unit force - push or pull forces

  1. $4 \mathrm { N }$

  2. $0 \mathrm { N }$

  3. $20 \mathrm { N }$

  4. $8 \mathrm { N }$

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Correct Option: C
Explanation:

Given,

$|\vec F _1|=12N$
$|\vec F _2|=8N$

The resultant force on the body is 
$|\vec R|=\sqrt{F _1^2+F _2^2+2F _1F _2cos\theta}$

For maximum value, $cos\theta=1$
$|\vec R|=\sqrt{(12)^2+(8)^2+2\times 12\times 8\times 1}$

$|\vec R _{max}|=\sqrt{144+64+24\times 8}$

$|\vec R _{max}|=\sqrt{400}=20N$
The correct option is C.

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

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

  1. Yes

  2. No

  3. Can't say

  4. None

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Correct Option: A
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.

Reference to ability of an object to return to its original position after it has been tilted slightly is termed as:

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

  1. Stability

  2. Equilibrium

  3. Centre of gravity

  4. Torque

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Correct Option: A
Explanation:

stability of an object depends on the ability of an object to return back to its original equlibirum, when disturbed

If you place pivot at center of a meter rule, weight has no

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

  1. property

  2. Concern

  3. Turning effect

  4. Magnitude

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Correct Option: C
Explanation:

The weight of an object is concentrated at the centre of gravity and hence a pivot at the centre of the metre scale does not record any changes in mass. Hence the scale does not turn around