00. Centre of Mass
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Rotational Motion

149731 A body of mass \(M_{1}=4 \mathrm{~kg}\) moves at \(5 \mathrm{~m} / \mathrm{s}\) and another body of mass \(M_{2}=2 \mathrm{~kg}\) moves at \(10 \mathrm{~m} / \mathrm{s}\). The kinetic energy of centre of mass is

1 \(\frac{200}{3} \mathrm{~J}\)
2 \(\frac{500}{3} \mathrm{~J}\)
3 \(\frac{400}{3} \mathrm{~J}\)
4 \(\frac{800}{3} \mathrm{~J}\)
JIPMER-2012
Rotational Motion

149732 The density of a rod having length \(l\) varies as \(\rho\) \(=c+D x\), where \(x\) is the distance from the left end. The centre of mass is

1 \(\frac{3 \mathrm{c} l+2 \mathrm{D} l^{2}}{3\left(2 \mathrm{c}+\mathrm{D} l^{2}\right)}\)
2 \(\frac{2 \mathrm{c} l+3 \mathrm{D} l^{2}}{2(4 \mathrm{c}+8 l)}\)
3 \(\frac{2 \mathrm{c} l+3 \mathrm{D} l^{2}}{3(2 \mathrm{c}+l)}\)
4 \(\frac{\mathrm{c} l+\mathrm{D} l^{2}}{3(2 \mathrm{c}+\mathrm{D} l)}\)
JIPMER-2015
Rotational Motion

149733 Find the \(x\) and \(y\) coordinates of the centre of mass of the three particles system (as shown).

1 \(1.0 \mathrm{~m}, 1.0 \mathrm{~m}\)
2 \(1.3 \mathrm{~m}, 0.9 \mathrm{~m}\)
3 \(1.1 \mathrm{~m}, 1.3 \mathrm{~m}\)
4 \(1.3 \mathrm{~m}, 1.1 \mathrm{~m}\)
AMU-2016
Rotational Motion

149737 Particles of masses \(\mathrm{m}, 2 \mathrm{~m}, 3 \mathrm{~m}\).... \(\mathrm{nm}\) gram are placed on the same line at distance \(l, 2 l, 3 l \ldots . \mathrm{n} l\) cm from a fixed point. The distance of centre of mass of the particles from the fixed point in \(\mathrm{cm}\) is

1 \(\frac{(2 \mathrm{n}+1) l}{3}\)
2 \(\frac{l}{\mathrm{n}+1}\)
3 \(\frac{\mathrm{n}\left(\mathrm{n}^{2}+1\right) l}{2}\)
4 \(\frac{2 l}{\mathrm{n}\left(\mathrm{n}^{2}+1\right)}\)
EAMCET-2002
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Rotational Motion

149731 A body of mass \(M_{1}=4 \mathrm{~kg}\) moves at \(5 \mathrm{~m} / \mathrm{s}\) and another body of mass \(M_{2}=2 \mathrm{~kg}\) moves at \(10 \mathrm{~m} / \mathrm{s}\). The kinetic energy of centre of mass is

1 \(\frac{200}{3} \mathrm{~J}\)
2 \(\frac{500}{3} \mathrm{~J}\)
3 \(\frac{400}{3} \mathrm{~J}\)
4 \(\frac{800}{3} \mathrm{~J}\)
JIPMER-2012
Rotational Motion

149732 The density of a rod having length \(l\) varies as \(\rho\) \(=c+D x\), where \(x\) is the distance from the left end. The centre of mass is

1 \(\frac{3 \mathrm{c} l+2 \mathrm{D} l^{2}}{3\left(2 \mathrm{c}+\mathrm{D} l^{2}\right)}\)
2 \(\frac{2 \mathrm{c} l+3 \mathrm{D} l^{2}}{2(4 \mathrm{c}+8 l)}\)
3 \(\frac{2 \mathrm{c} l+3 \mathrm{D} l^{2}}{3(2 \mathrm{c}+l)}\)
4 \(\frac{\mathrm{c} l+\mathrm{D} l^{2}}{3(2 \mathrm{c}+\mathrm{D} l)}\)
JIPMER-2015
Rotational Motion

149733 Find the \(x\) and \(y\) coordinates of the centre of mass of the three particles system (as shown).

1 \(1.0 \mathrm{~m}, 1.0 \mathrm{~m}\)
2 \(1.3 \mathrm{~m}, 0.9 \mathrm{~m}\)
3 \(1.1 \mathrm{~m}, 1.3 \mathrm{~m}\)
4 \(1.3 \mathrm{~m}, 1.1 \mathrm{~m}\)
AMU-2016
Rotational Motion

149737 Particles of masses \(\mathrm{m}, 2 \mathrm{~m}, 3 \mathrm{~m}\).... \(\mathrm{nm}\) gram are placed on the same line at distance \(l, 2 l, 3 l \ldots . \mathrm{n} l\) cm from a fixed point. The distance of centre of mass of the particles from the fixed point in \(\mathrm{cm}\) is

1 \(\frac{(2 \mathrm{n}+1) l}{3}\)
2 \(\frac{l}{\mathrm{n}+1}\)
3 \(\frac{\mathrm{n}\left(\mathrm{n}^{2}+1\right) l}{2}\)
4 \(\frac{2 l}{\mathrm{n}\left(\mathrm{n}^{2}+1\right)}\)
EAMCET-2002
NEET DIGITAL LIBRARY
Rotational Motion

149731 A body of mass \(M_{1}=4 \mathrm{~kg}\) moves at \(5 \mathrm{~m} / \mathrm{s}\) and another body of mass \(M_{2}=2 \mathrm{~kg}\) moves at \(10 \mathrm{~m} / \mathrm{s}\). The kinetic energy of centre of mass is

1 \(\frac{200}{3} \mathrm{~J}\)
2 \(\frac{500}{3} \mathrm{~J}\)
3 \(\frac{400}{3} \mathrm{~J}\)
4 \(\frac{800}{3} \mathrm{~J}\)
JIPMER-2012
Rotational Motion

149732 The density of a rod having length \(l\) varies as \(\rho\) \(=c+D x\), where \(x\) is the distance from the left end. The centre of mass is

1 \(\frac{3 \mathrm{c} l+2 \mathrm{D} l^{2}}{3\left(2 \mathrm{c}+\mathrm{D} l^{2}\right)}\)
2 \(\frac{2 \mathrm{c} l+3 \mathrm{D} l^{2}}{2(4 \mathrm{c}+8 l)}\)
3 \(\frac{2 \mathrm{c} l+3 \mathrm{D} l^{2}}{3(2 \mathrm{c}+l)}\)
4 \(\frac{\mathrm{c} l+\mathrm{D} l^{2}}{3(2 \mathrm{c}+\mathrm{D} l)}\)
JIPMER-2015
Rotational Motion

149733 Find the \(x\) and \(y\) coordinates of the centre of mass of the three particles system (as shown).

1 \(1.0 \mathrm{~m}, 1.0 \mathrm{~m}\)
2 \(1.3 \mathrm{~m}, 0.9 \mathrm{~m}\)
3 \(1.1 \mathrm{~m}, 1.3 \mathrm{~m}\)
4 \(1.3 \mathrm{~m}, 1.1 \mathrm{~m}\)
AMU-2016
Rotational Motion

149737 Particles of masses \(\mathrm{m}, 2 \mathrm{~m}, 3 \mathrm{~m}\).... \(\mathrm{nm}\) gram are placed on the same line at distance \(l, 2 l, 3 l \ldots . \mathrm{n} l\) cm from a fixed point. The distance of centre of mass of the particles from the fixed point in \(\mathrm{cm}\) is

1 \(\frac{(2 \mathrm{n}+1) l}{3}\)
2 \(\frac{l}{\mathrm{n}+1}\)
3 \(\frac{\mathrm{n}\left(\mathrm{n}^{2}+1\right) l}{2}\)
4 \(\frac{2 l}{\mathrm{n}\left(\mathrm{n}^{2}+1\right)}\)
EAMCET-2002
Join With Us for More Updates
Rotational Motion

149731 A body of mass \(M_{1}=4 \mathrm{~kg}\) moves at \(5 \mathrm{~m} / \mathrm{s}\) and another body of mass \(M_{2}=2 \mathrm{~kg}\) moves at \(10 \mathrm{~m} / \mathrm{s}\). The kinetic energy of centre of mass is

1 \(\frac{200}{3} \mathrm{~J}\)
2 \(\frac{500}{3} \mathrm{~J}\)
3 \(\frac{400}{3} \mathrm{~J}\)
4 \(\frac{800}{3} \mathrm{~J}\)
JIPMER-2012
Rotational Motion

149732 The density of a rod having length \(l\) varies as \(\rho\) \(=c+D x\), where \(x\) is the distance from the left end. The centre of mass is

1 \(\frac{3 \mathrm{c} l+2 \mathrm{D} l^{2}}{3\left(2 \mathrm{c}+\mathrm{D} l^{2}\right)}\)
2 \(\frac{2 \mathrm{c} l+3 \mathrm{D} l^{2}}{2(4 \mathrm{c}+8 l)}\)
3 \(\frac{2 \mathrm{c} l+3 \mathrm{D} l^{2}}{3(2 \mathrm{c}+l)}\)
4 \(\frac{\mathrm{c} l+\mathrm{D} l^{2}}{3(2 \mathrm{c}+\mathrm{D} l)}\)
JIPMER-2015
Rotational Motion

149733 Find the \(x\) and \(y\) coordinates of the centre of mass of the three particles system (as shown).

1 \(1.0 \mathrm{~m}, 1.0 \mathrm{~m}\)
2 \(1.3 \mathrm{~m}, 0.9 \mathrm{~m}\)
3 \(1.1 \mathrm{~m}, 1.3 \mathrm{~m}\)
4 \(1.3 \mathrm{~m}, 1.1 \mathrm{~m}\)
AMU-2016
Rotational Motion

149737 Particles of masses \(\mathrm{m}, 2 \mathrm{~m}, 3 \mathrm{~m}\).... \(\mathrm{nm}\) gram are placed on the same line at distance \(l, 2 l, 3 l \ldots . \mathrm{n} l\) cm from a fixed point. The distance of centre of mass of the particles from the fixed point in \(\mathrm{cm}\) is

1 \(\frac{(2 \mathrm{n}+1) l}{3}\)
2 \(\frac{l}{\mathrm{n}+1}\)
3 \(\frac{\mathrm{n}\left(\mathrm{n}^{2}+1\right) l}{2}\)
4 \(\frac{2 l}{\mathrm{n}\left(\mathrm{n}^{2}+1\right)}\)
EAMCET-2002
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here