The position vector of three particles of masses $1\, kg, 2\, kg$ and $3\, kg$ are $\overrightarrow {{r_1}} = (\widehat i + 4\widehat j + \widehat k)\,m,\overrightarrow {{r_2}} = (\widehat i + \widehat j + \widehat k)\,m$ and $\overrightarrow {{r_3}} = (2\widehat i - \widehat j - 2\widehat k)\,m$ respectively. The position vector of their centre of mass is
The position vector of three particles of masses $1\, kg, 2\, kg$ and $3\, kg$ are $\overrightarrow {{r_1}} = (\widehat i + 4\widehat j + \widehat k)\,m,\overrightarrow {{r_2}} = (\widehat i + \widehat j + \widehat k)\,m$ and $\overrightarrow {{r_3}} = (2\widehat i - \widehat j - 2\widehat k)\,m$ respectively. The position vector of their centre of mass is
- A
$\frac{1}{2}(3\widehat i + \widehat j - \widehat k)\,m$
- B
$\frac{1}{2}(\widehat i +3 \widehat j - 2 \widehat k)\,m$
- C
$\frac{1}{4}(3\widehat i - \widehat j + \widehat k)\,m$
- D
$\frac{1}{4}(\widehat i - 3 \widehat j + \widehat k)\,m$
Similar Questions
A firecracker is thrown with velocity of $30 \,ms ^{-1}$ in a direction which makes an angle of $75^{\circ}$ with the vertical axis. At some point on its trajectory, the firecracker splits into two identical pieces in such a way that one piece falls $27 \,m$ far from the shooting point. Assuming that all trajectories are contained in the same plane, how far will the other piece fall from the shooting point? (Take, $g=10 \,ms ^{-2}$ and neglect air resistance)
A firecracker is thrown with velocity of $30 \,ms ^{-1}$ in a direction which makes an angle of $75^{\circ}$ with the vertical axis. At some point on its trajectory, the firecracker splits into two identical pieces in such a way that one piece falls $27 \,m$ far from the shooting point. Assuming that all trajectories are contained in the same plane, how far will the other piece fall from the shooting point? (Take, $g=10 \,ms ^{-2}$ and neglect air resistance)
- [KVPY 2012]
Sector of a circular plate shown in figure has position of centre of mass at $y_{CM} =$
Sector of a circular plate shown in figure has position of centre of mass at $y_{CM} =$
Two bodies of mass $1\,kg$ and $3\,kg$ have position vectors $\hat{i}+2 \hat{j}+\hat{k}$ and $-3 \hat{i}-2 \hat{j}+\hat{k}$ respectively.The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector.
- [AIPMT 2009]
From a uniform disk of radius $R$, a circular hole of radius $R/2$ is cut out. The centre of the hole is at $R/2$ from the centre of the original disc. Locate the centre of gravity of the resulting flat body.
From a uniform disk of radius $R$, a circular hole of radius $R/2$ is cut out. The centre of the hole is at $R/2$ from the centre of the original disc. Locate the centre of gravity of the resulting flat body.
A narrow but tall cabin is falling freely near the earth's surface. Inside the cabin, two small stones $A$ and $B$ are released from rest (relative to the cabin). Initially $A$ is much above the centre of mass and $B$ much below the centre of mass of the cabin. A close observation of the motion of $A$ and $B$ will reveal that
A narrow but tall cabin is falling freely near the earth's surface. Inside the cabin, two small stones $A$ and $B$ are released from rest (relative to the cabin). Initially $A$ is much above the centre of mass and $B$ much below the centre of mass of the cabin. A close observation of the motion of $A$ and $B$ will reveal that
- [KVPY 2011]