Class 11th

A bullet of 10g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m/s. The length of the pendulum is 0.5m and mass of the bob is 1kg. The minimum value of v = _____m/s so that the pendulum describes a circle.

(Assume the string to be inextensible and g = 10 m/s²)

The number of water molecules in gypsum, dead burnt plaster and plaster of paris, respectively are:

Two simple harmonic motion, are represented by the equations y₁ = 10sin $\left(3\pi t+\frac{\pi }{3}\right)$ $y_2=5\left(sin3\pi t+\sqrt[]{3}cos3\pi t\right)$  

Ratio of amplitude of y₁ to y₂ = x:1. The value of x is_______ 

A tuning fork is vibrating at 250 Hz. The length of the shortest closest organ pipe that will resonate with the tuning fork will be_____cm.

(Take speed of sound in air as 340 ms^-1)

A car is moving on a plane inclined at 30° to the horizontal with an acceleration of 10ms^-2 parallel to the upward. A bob is suspended by a string from the roof of the car. The angle in degree which the string makes with the vertical is______. (Take g = 10ms^-2)

A heat engine operates between a cold reservoir at temperature T₂ = 400K and a hot reservoir at temperature T₁. It takes 300J of heat from the hot reservoir and delivers 240J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be________K.

Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.

If the rms speed of oxygen molecules at 0°C is 160 m/s, find the rms speed of hydrogen molecules at 0°C.

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45° and 60° with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is $\frac{1}{\sqrt[]{x}}.$  The value of x is

If the velocity of a body related to displacement x is given by $\upsilon =\sqrt[]{5000+24x}m/s,$  then the acceleration of the body is…….