Tag: turning effects of forces

Quizzes (7) Questions (109)

Questions Related to turning effects of forces

Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

The centre of mass of a body:

  1. Lies always at the geometrical center

  2. Lies always inside the body

  3. Lies always outside the body

  4. Lies within or outside the body
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The centre of mass of a body can lie within or outside the body.

For example, centre of mass of a uniform rod lies at its geometrical centre which lies within the rod whereas centre of mass of a uniform ring lies at its geometrical centre which lies outside the ring.

Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

Two unequal masses are tied together with a cord with a compressed spring in between.
Which one is correct?

  1. Both masses will have equal KE.

  2. Lighter block will have greater KE.

  3. Heavier block will have greater KE.

  4. None of above answers is correct.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Lighter block will have greater kinetic energy to lighter block will have higher velocity mass so Heavier block, hence by equation $\dfrac{1}{2}mv^2,$ the lighter will have greater KE.
Hence, the answer is Lighter block will have greater KE.

Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

A string is wrapped around a cylinder of mass $M$ and radius $R$. The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder unwinds the string, The work done on the cylinder for reaching an angular speed $\omega$ is:

  1. $\cfrac { 2M{ R }^{ 2 }{ \omega }^{ 2 } }{ 3 } $

  2. $\cfrac { M{ R }^{ 2 }{ \omega }^{ 2 } }{ 3 } $

  3. $\cfrac { M{ R }^{ 2 }{ \omega }^{ 2 } }{ 2 } $

  4. $\cfrac { M{ R }^{ 2 }{ \omega }^{ 2 } }{ 4 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Work done is the rotational KE acquired be cylinder,
$=\dfrac{1}{2} I\omega ^2$
$=\dfrac{1}{2}\dfrac{MR^2}{2}\omega ^2$
$=\dfrac{MR^2}{4}\omega ^2.$
Hence, the answer is $\dfrac{MR^2}{4}\omega ^2.$

Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

A straight rod of length L has one of its ends at the origin and the other at $x=L$. If the mass per unit length of the rod is given by Ax where A is constant, where is its mass centre?

  1. $L/3$

  2. $L/2$

  3. $2L/3$

  4. $3L/4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
I assume you meant to say "a is a CONSTANT".

xc = coordinate of center of mass

M = total mass

$xc = ∫xdm / ∫dm = ∫xdm / M$

Given:$ m(x) = ax ⇒ dm/dx = a ⇒ dm = adx$

$∫xdm = ∫01 x(adx) = a/2$

$M = ∫dm = ∫(dm/dx)dx = ∫01 adx = a$

$xc = (a/2)/a = 1/2$

By the way, this is a mechanics problem (in statics), not a thermodynamics problem.

 

Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ fromthe centre of the bigger disc. The value of $\alpha$ is

  1. $\cfrac{1}{2}$

  2. $\cfrac{1}{6}$

  3. $\cfrac{1}{4}$

  4. $\cfrac{1}{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the negative mass method, the center of mass of the remaining part is found by subtracting the mass and moment of the smaller disc from the larger one. The calculation leads to alpha = 1/3.

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

State whether given statement is True or False.

Centre of gravity of a freely suspended body always lies vertically below the point of suspension.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Yes, Centre of gravity of a freely suspended body always lies vertically below the point of suspension. The center of gravity of an object is the point you can suspend the object from without there being any rotation because of the force of gravity, no matter how the object is oriented. If you suspend an object from any point, let it go and allow it to come to rest, the center of gravity will lie along a vertical line that passes through the point of suspension. Unless you've been exceedingly careful in balancing the object, the center of gravity will generally lie below the suspension point.

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

Where is the centre of gravity of a uniform ring situated ?

  1. At the centre of ring.

  2. At the centre of semicircular ring

  3. At the centre of radius

  4. cant say
Reveal answer Fill a bubble to check yourself
A 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 bodies centre of gravity lies at the centre of the body.Hence we know that there will be a centre for a uniform ring lamina.Hence this centre of the ring will be centre of gravity.

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

Stability and center of gravity of an object whose stability can be increased by

  1. lowering center of gravity and increasing area of base

  2. lowering center of gravity and decreasing area of base

  3. moving center of gravity higher and increasing areas of base

  4. moving center of gravity higher and decreasing area of base
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The position of the centre of gravity of an object affects its stability. The lower the centre of gravity is, the more stable the object. The higher it is the more likely the object is to topple over if it is pushed.
In general, increasing the size of the base (that is area) of support increases stability.