Tag: acceleration due to gravity

Questions Related to acceleration due to gravity

AU the particles of a system are situated at a distance r from the origin. The distance of the centre of mass of the system from the origin is :

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

  1. = r

  2. $\leq \, r$

  3. $> r$

  4. $\leq 0$

Show answer
Correct Option: B
Explanation:

The largest distance between the origin and center of mass would be 'r' when there is only one particle.
If there are more than one particle, the center of mass would be inside the circle of radius 'r' centered at the origin.
Hence option B is correct.

The position vector of three particles of masses $m _1\, =\,1kg,\, m _2\, =\, 2\, kg$ and $m _3\, =\, 3\, kg$ are $\vec{r} _1\, =\, (\hat{i}\, +\, 4\hat{j}\, +\, \hat{k})\, m,\, \vec{r} _2\, =\, (\hat{i}\, +\, \hat{j}\, +\, \hat{k}) m$ and $\vec{r} _3\, =\, (2\hat{i}\, -\, \hat{j}\, -\, 2\hat{k})$ m respectively. Find the position vector of their center of mass.

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

  1. $\displaystyle \frac {1}{2}\, (\hat{i}\, +\, \hat{j}\, -\, \hat{k})\, m$

  2. $\displaystyle \frac {1}{2}\, (\hat{i}\, +\, 3\hat{j}\, -\, \hat{k})\, m$

  3. $\displaystyle \frac {1}{2}\, (\hat{i}\, +\, \hat{j}\, -\, 3\hat{k})\, m$

  4. $\displaystyle \frac {1}{2}\, (3\hat{i}\, +\, \hat{j}\, -\, \hat{k})\, m$

Show answer
Correct Option: D
Explanation:

The position vector of COM of the.three particles will be given by
$\vec{r} _{COM}\, =\, \displaystyle \frac {m _1\vec{r} _1\, +\, m _2\vec{r} _2\, +\, m _3\vec{r} _3}{m _1\, +\, m _2\, +\, m _3}$
Substituting the values, we get
$\vec{r} _{COM}\, =\, \displaystyle \frac {(1) (\hat{i}\, +\, 4\hat{j}\, +\, \hat{k})\, +\, (2) (\hat{i}\, +\, \hat{j}\, +\, \hat{k})\, +\, (3) (2\hat{i}\, -\, \hat{j}\, -\, 2\hat{k})}{1+2+3}\, =\, \displaystyle \frac {1}{2}\, (3\hat{i}\, +\, \hat{j}\, -\, \hat{k})\, m$.
Hence, the position vector of their center of mass is $\, \displaystyle \frac {1}{2}\, (3\hat{i}\, +\, \hat{j}\, -\, \hat{k})\, m$.

At which point is the centre of gravity situated in: A circular lamina.

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

  1. At the centre of radius.

  2. At the centre of semi circular lamina.

  3. At the centre of circular lamina.

  4. can not say

Show answer
Correct Option: C
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 this will be at the centre of the circular lamina.

What is the position of centre of gravity of a rectangular lamina?

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

  1. At the mid point of longer side

  2. At the mid point of shorter side

  3. At the point of intersection of its diagonals

  4. At one of the corners

Show answer
Correct Option: C
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. Hence for a regular shaped bodies it will have at the centre of that body. Hence for a rectangle it is nothing but at the point of intersection of diagonals.

At which point is the centre of gravity situated in: A triangular lamina

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

  1. At the point of intersection of its perpendicular bisectors.

  2. At the point of intersection of its angular bisectors.

  3. At the point of intersection of its sides

  4. At the point of intersection of its medians.

Show answer
Correct Option: D
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 centre of gravity lies in the centre of the particular body. Hence for triangular lamina centre lies at the centroid which is the intersection of the three lines drawn from the vertex to the midpoint of the opposite side. Hence centre of gravity lies at the intersection of the three medians.

A body of mass 2 $ \mathrm{kg}  $ is thrown up vertically with $ \mathrm{K.E.}  $ of 490 Joules. If the acceleration due to gravity is 9.8 $ \mathrm{m} / \mathrm{s}^{2}  $ , then the height at which the K.E. of the body becomes half its originalvalue is given by

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

  1.  $50m$

  2.  $12.5m$

  3. $25m$

  4.  $10m$

Show answer
Correct Option: B

People can spin a ball on their finger. This is due to

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

  1. the centre of gravity of the ball is on his finger.

  2. the resultant force is passing through the centre of gravity of the ball.

  3. the resultant force is passing through the centre of the ball.

  4. both A and B

Show answer
Correct Option: D
Explanation:

let us assume body of mass m and divide it into many small particles. The centre of mass means it is the mean value of the all the small particles . it would more clear by assuming the body in 3-D coordinate system and calculate its mean of all small particles with the co ordinates in three dimension . where as the centre of gravity is also same but it is the mean of its weight. it is the point were total weight acts


we may think  both be same but not always. because in above example the value of g will be different at different positions because of that while calculating the mean the centre will shifts from centre of mass


in the question given the centre of mass will be exact center of ball and centre of gravity also lies at the center of mass as the ball is small there will be no greater effect by g. so the the centre of gravity of ball is on finger and resultant force is weight which is all acts on center of ball

If we suspend lamina at different positions, its center of gravity will still lie along the :

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

  1. plumb line

  2. line of force

  3. line of weight

  4. gravity line

Show answer
Correct Option: A
Explanation:

let us assume body of mass m and divide it into many small particles. The centre of mass means it is the mean value of the all the small particles . it would more clear by assuming the body in 3-D coordinate system and calculate its mean of all small particles with the co ordinates in three dimension . where as the centre of gravity is also same but it is the mean of its weight. it is the point were total weight acts

we may think  both be same but not always. because in above example the value of g will be different at different positions because of that while calculating the mean the centre will shifts from centre of mass 
  because  suspension of the body at the different position the value of g value effects at some point so the centre of gravity will shifts but stays along blub line



Which of following statements related to center of gravity is/are false?

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

  1. If an object is placed in a uniform gravitational field, center of gravity coincides with center of mass.

  2. The center of gravity of an object is defined as point through which its whole weight appears to act.

  3. The center of gravity is sometimes confused with center of mass.

  4. The center of gravity always lies inside object.

Show answer
Correct Option: D
Explanation:

Center of gravity need not always lie inside object. Suppose take a ring. Its center of mass lies at its center. Hence it is not inside the ring but it is outside the body of the ring ie. at its center. All the other statements are correct.

Around the centre of gravity ______ vanishes. Fill in the blank. 
physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity
  1. Resultant acceleration due to gravity force

  2. Resultant velocity due to gravity force

  3. Resultant torque due to gravity force

  4. None

Show answer
Correct Option: C
Explanation:

Resultant torque due to gravity force vanishes around the centre of gravity because perpendicular distance between the gravitational force and the point about that toque is calculated becomes very very small or almost zero.