Q. No.The centre of the mass of \(3\) particles, \(10\) kg, \(20\) kg, and \(30\) kg, is at \((0,0,0)\). Where should a particle with a mass of \(40\) kg be placed so that its combined centre of mass is \((3,3,3)\)?
1. \((0,0,0)\)
2. \((7.5, 7.5, 7.5)\)
3. \((1,2,3)\)
4. \((4,4,4)\)
1. \((0,0,0)\)
2. \((7.5, 7.5, 7.5)\)
3. \((1,2,3)\)
4. \((4,4,4)\)
The position of a particle is given by \(\vec r = \hat i+2\hat j-\hat k\) and momentum \(\vec P = (3 \hat i + 4\hat j - 2\hat k)\). The angular momentum is perpendicular to:
| 1. | X-axis |
| 2. | Y-axis |
| 3. | Z-axis |
| 4. | Line at equal angles to all the three axes |
A wheel with a radius of \(20\) cm has forces applied to it as shown in the figure. The torque produced by the forces of \(4\) N at \(A\), \(8~\)N at \(B\), \(6\) N at \(C\), and \(9~\)N at \(D\), at the angles indicated, is:
1. \(5.4\) N-m anticlockwise
2. \(1.80\) N-m clockwise
3. \(2.0\) N-m clockwise
4. \(3.6\) N-m clockwise
A particle of mass m moves in the XY plane with a velocity of V along the straight line AB. If the angular momentum of the particle about the origin O is LA when it is at A and LB when it is at B, then:
| 1. | \(\mathrm{L}_{\mathrm{A}}>\mathrm{L}_{\mathrm{B}}\) |
| 2. | \(\mathrm{L}_{\mathrm{A}}=\mathrm{L}_{\mathrm{B}}\) |
| 3. | The relationship between \(\mathrm{L}_{\mathrm{A}} \text { and } \mathrm{L}_{\mathrm{B}}\) depends upon the slope of the line AB |
| 4. | \(\mathrm{L}_{\mathrm{A}}<\mathrm{L}_{\mathrm{B}}\) |
A wheel is rotating about an axis through its centre at \(720\) r.p.m. It is acted upon by a constant torque opposing its motion for \(8\) seconds to bring it to rest finally.
The value of torque in N-m is: (given \(I\) = kg )
1. \(48\)
2. \(72\)
3. \(96\)
4. \(120\)
For L = 3.0 m, the total torque about pivot A provided by the forces as shown in the figure is:
| 1. | 210 Nm | 2. | 140 Nm |
| 3. | 95 Nm | 4. | 75 Nm |
Two rotating bodies A and B of masses m and 2m with moments of inertia and have equal kinetic energy of rotation. If and be their angular momenta respectively, then:
1.
2.
3.
4.
The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:
1. B
2. C
3. D
4. A
1. \(\frac{m_1m_2}{m_1+m_2}l^2\)
2. \(\frac{m_1+m_2}{m_1m_2}l^2\)
3. \((m_1+m_2)l^2\)
4. \(\sqrt{(m_1m_2)}l^2\)
| 1. | \(wx \over d\) | 2. | \(wd \over x\) |
| 3. | \(w(d-x) \over x\) | 4. | \(w(d-x) \over d\) |
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