TS EAMCET · Physics · Oscillations
A small sphere of radius \(r\) is placed as a concave surface of radius of curvature \(R\) a little away from the centre. When the sphere is released, it oscillates. Assuming, the oscillation to be simple harmonic motion and \(r< < R\), then the time period is
- A \(2 \pi \sqrt{\frac{R}{g}}\)
- B \(2 \pi \sqrt{\frac{3 R}{2 g}}\)
- C \(2 \pi \sqrt{\frac{2 R}{3 g}}\)
- D \(2 \pi \sqrt{\frac{R}{2 g}}\)
Answer & Solution
Correct Answer
(A) \(2 \pi \sqrt{\frac{R}{g}}\)
Step-by-step Solution
Detailed explanation
The motion of sphere is as shown in figure As, the sphere has simple harmonic motion on a curved surface, which is equivalent to the motion of pendulum. So, its time period is \(T=2 \pi \sqrt{\frac{l}{g}}\) Here, \(l=R\) \(\therefore \quad T=2 \pi \sqrt{\frac{R}{g}}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Two wires \(A\) and \(B\) of same length, same radius and same Young's modulus are heated to same range of temperatures. If the coefficient of linear expansion of A is \(\frac{3}{2}\) times that of \(\mathrm{B}\), then the ratio of the thermal stresses produced in the two wires A and B isTS EAMCET 2023 Medium
- The terminal velocity of a liquid drop of radius ' \(r\) ' falling through air is \(v\). If two such drops are combined to form a bigger drop, the terminal velocity with which the bigger drop falls through air is (ignore any buoyant force due to air)TS EAMCET 2013 Medium
- Consider an object kept at the centre, in the \(X Y\)-plane, on which five coplanar forces act as shown in the figure. The resultant force on the object is
TS EAMCET 2018 Medium - A body is projected from the earth's surface with a speed \(\sqrt{5}\) times the escape speed \(\left(\mathrm{V}_{\mathrm{e}}\right)\). The speed of the body when it escapes from the gravitational influence of the earth isTS EAMCET 2025 Medium
- A block of mass 0.5 kg is at rest on a horizontal table. The coefficient of kinetic friction between the table and the block is 0.2 . If a horizontal force of 5 N is applied on the block, the kinetic energy of the block in a time of 4 s is (Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) ),TS EAMCET 2024 Medium
- A transmitting and receiving antenna have height of \(d\) metres each. The maximum distance between them for satisfactory communication in Line-of-Sight mode (LOS) is \(2 d\) kilometers. If the radius of earth is \(6400 \mathrm{~km}\), then the value of \(d\) isTS EAMCET 2018 Medium
More PYQs from TS EAMCET
- In the circuit given below, the capacitor is charged by closing the switch and opening the switch . After charging, the switch is opened and is closed, then the maximum current in the circuit
TS EAMCET 2018 Easy - A wheel of radius with 0.5 m and a moment of inertia of 10 kg. m2 is rotating freely at an angular speed of 70 rev/min. The wheel can be stopped in 5.0 s by pressing a wet cloth against the rim and exerting a radially inward force of 88 N. The coefficient of kinetic friction between the wheel and wet cloth isTS EAMCET 2022 Hard
- The ratio of the radii of two solid spheres of same mass is \(2: 3\). The ratio of the moments of inertia of the spitıres about their diameters isTS EAMCET 2023 Easy
- A block of mass \(2 \mathrm{~kg}\) is connected to an ideal spring and is placed on a smooth horizontal surface. The spring is pulled to move the block and at an instant, the speed of end \(A\) of the spring and speed of the block were measured to be \(6 \mathrm{~m} / \mathrm{s}\) and \(3 \mathrm{~m} / \mathrm{s}\), respectively. At this moment the potential energy stored in the spring in increasing at a rate \(15 \mathrm{~J} / \mathrm{s}\). Find the acceleration of the block at this instant.
TS EAMCET 2019 Easy - A cylindrical vessel is filled with water upto the height \(1 \mathrm{~m}\) from the base. A small orifice is opened at some height in the cylinder and the water level is reduced to height of orifice in \(20 \mathrm{~s}\). If the base area of the cylinder is 100 times the area of orifice, then the height of orifice from the base is (take, \(g=10 \mathrm{~m} / \mathrm{s}^2\) )TS EAMCET 2018 Medium
- A small block of mass \(5 \mathrm{~g}\) and charge \(5 \mu \mathrm{C}\) is placed on insulated, frictionless, inclined plane of angle \(60^{\circ}\). An electric field is applied parallel to the inclined plane. If the block remains at rest then the magnitude of electric field is \(\left[\right.\) Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\))TS EAMCET 2022 Easy