Class 11th

The given arrangement is in vertical plane and initially the springs are in natural length. The uniform rod is hinged at end O, about which it can freely rotate. The angular frequency of small oscillations of the rod is n/8 √(k/m). Find n. (Given: m = mass of rod, L = length of rod and k = mg/L)

A sine wave is travelling in a medium. The minimum distance between the two particles, always having same speed, is

A free particle having one electronic charge with initial kinetic energy 9 eV and de Broglie wavelength 1 mm enters a region of V₀ potential difference such that new de Broglie wavelength is now 1.5 mm. Then eV₀ is

A uniform rod, of mass m, length l and r radius of cross section, is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity ω in horizontal plane. If Y is the Young's modulus of the material of rod, the increase in its length due to rotation of rod is

A ball of mass 0.15 kg is dropped from a height. 10 m, strikes the ground and rehounds to the same height. The magnitude of impulse imparted to the ball is (g = 10 m/s² ) nearly:

A solid circular disc (m, R) translates with V? and rotates with ω? = 2V₀/R at t = 0. Because of friction, pure rolling starts at t = t₀. The coefficient of friction is μ. Find t₀.

A particle of mass ' m ' is projected with a velocity v = kVe(k < 1) from the surface of the earth.
(Ve = escape velocity)
The maximum height above the surface reached by the particle is:

A car starts from rest and accelerates at 5 m/s². At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at
t = 6 s ? (Take g = 10 m/s² )

A uniform rod of length 200 cm and mass 500 g balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 A and another unknown mass 'm' is suspended the rod at 160 cm mark as shown in the Find the value of ' m ' such that the
rod is in equilibrium. (g = 10 m/s²)

From a circular ring of mass ' M ' and radius ' R ' an arc corresponding to a 90° 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 ' MR² '. Then the value of ' K ' is: