A uniform rod of length \(200~ \text{cm}\) and mass \(500~ \text g\) is balanced on a wedge placed at \(40~ \text{cm}\) mark. A mass of \(2~\text{kg}\) is suspended from the rod at \(20~ \text{cm}\) and another unknown mass \(m\) is suspended from the rod at \(160~\text{cm}\) mark as shown in the figure. What would be the value of \(m\) such that the rod is in equilibrium? (Take \(g=10~( \text {m/s}^2)\)
1. | \({\dfrac 1 6}~\text{kg}\) | 2. | \({\dfrac 1 {12}}~ \text{kg}\) |
3. | \({\dfrac 1 2}~ \text{kg}\) | 4. | \({\dfrac 1 3}~ \text{kg}\) |
From a circular ring of mass \({M}\) and radius \(R\), an arc corresponding to a \(90^\circ\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \(K\) times \(MR^2\). The value of \(K\) will be:
1. | \(\dfrac{1}{4}\) | 2. | \(\dfrac{1}{8}\) |
3. | \(\dfrac{3}{4}\) | 4. | \(\dfrac{7}{8}\) |
A thin circular ring \(\mathrm{M}\) and radius \(\mathrm{r}\) is rotating about its axis with a constant angular velocity ω. Four objects, each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be:
1.
2.
3.
4.
1. | \(1.5\) m | 2. | \(2\) m |
3. | \(2.5\) m | 4. | \(3.0\) m |
When a stick is released (as shown in the figure below), its free end velocity when it strikes the ground is:
1. 4.2 m/s
2. 1.4 m/s
3. 2.8 m/s
4. m/s
For a body, with angular velocity \( \vec{\omega }=\hat{i}-2\hat{j}+3\hat{k}\) and radius vector \( \vec{r }=\hat{i}+\hat{j}++\hat{k},\) its velocity will be:
1. \(-5\hat{i}+2\hat{j}+3\hat{k}\)
2. \(-5\hat{i}+2\hat{j}-3\hat{k}\)
3. \(-5\hat{i}-2\hat{j}+3\hat{k}\)
4. \(-5\hat{i}-2\hat{j}-3\hat{k}\)
A disc is rotating with angular speed \(\omega.\) If a child sits on it, what is conserved here?
1. | Linear momentum | 2. | Angular momentum |
3. | Kinetic energy | 4. | Potential energy |
A circular disc is to be made by using iron and aluminium so that it acquires a maximum moment of inertia about its geometrical axis. It is possible with:
1. | Aluminium in the interior and iron surrounding it |
2. | Iron at the interior and aluminium surrounding it |
3. | Using iron and aluminium layers in alternate order |
4. | A sheet of iron is used at both the external surface and aluminium sheet as the internal layer |
Consider a system of two particles having masses m1 and m2. If the particle of mass m1 is pushed towards the mass centre of particles through a distance 'd', by what distance would the particle of mass m2 move so as to keep the mass centre of particles at the original position ?
1.
2. d
3.
4.
A wheel having a moment of inertia of \(2\) kg–m2 about its vertical axis rotates at the rate of \(60\) rpm about the axis. The torque which can stop the wheel's rotation in one minute would be:
1. | \(\dfrac{\pi }{12}\) N-m | 2. | \(\dfrac{\pi }{15}\) N-m |
3. | \(\dfrac{\pi }{18}\) N-m | 4. | \(\dfrac{2\pi }{15}\) N-m |