Class 11th

A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (take g = 9.8ms?²)

What will be the nature of flow of water form a circular tap, when its flow rate increased from 0.18L/min to 0.48L/min? The radius of the tap and viscosity of water are 0.5 cm and 10⁻³ Pa s, respectively. (Density of water: 10³ kg/m ³)

Calculate the value of mean free path (λ) for oxygen molecules at temperature 27° C and pressure 1.01*10⁵ Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 x 10⁻²³ JK⁻¹)

In order to determine the young's modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale of least count = 1 mm), a weight of mass 1 kg (measured using a scale of least count = 1g) was hanged to get the elongation of 0.5 cm (measured using a scale of least count 0.001 cm.) What will be the fractional error in the value of young's modulus determined by this experiment?

A mosquito is moving with a velocity v = 0.5t² i + 3t j + 9 k m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2s?

The velocity- displacement graph describing the motion of abicycle is shown in the figure. The acceleration displacement graph of the bicycle's motion is best described by:

Four equal masses, m each are placed at the corners of a square of length l as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be :

A particle executes simple harmonic motion represented by displacement function as x(t) = A sin(ωt + φ). If the position and velocity of the particle at t = 0s are 2cm and 2ω cm s?¹ respectively, then its amplitude is x√2 cm where the value of x is _____.

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias (I?/I?) will be x:1. The value of x will be _____.

A small block slides down from the top of hemisphere of radius R = 3m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is _____ m. (Assume there is no friction between the block and the hemisphere)