Mix Test - 2...

Water of mass m₂ = 1 kg is contained in a copper calorimeter of mass m₁ = 1 kg. Their common temperature t is 10°C. Now, a piece of ice of mass m₃ = 2 kg and temperature -11°C is dropped into the calorimeter. Neglecting any heat loss, the final temperature of the system is [Specific heat of copper = 0.1 Kcal/ kg°C, Specific heat of water = 1 Kcal/kg°C, Specific heat of ice = 0.5 Kcal/kg°C, Latent heat of fusion of ice = 78.7 Kcal/kg]

A particle is moving along the path given by (where C is a positive constant). The relation between the acceleration (a) and the velocity (v) of the particle, at t = 5 sec, is

'n' number of water droplets, each of radius r, coalesce to form a single drop of radius R. The rise in temperature d is (T is the surface tension, J is the energy equivalent)

Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle with AB. The moment of inertia of the plate about the axis CD is then equal to

Which of the following graphs represents current-voltage characteristics for a series combination?

An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is



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A sound source S and an observer O are placed as shown in the figure. Sound can reach the observer only by getting reflected by a reflector surface M, which is moving towards S along PS with a speed of 300 m/s. The angle OMS at any point is referred to as . What frequency will O perceive when = 127°? (Assume that the reflector is always able to reflect the sound towards the observer. Speed of sound = 400 m/s. Natural frequency of sound source = 400 Hz)

In the assembly shown in the figure below, both the pulleys are massless and frictionless on their axes. The positions of the strings are adjusted in such a way that, in equilibrium position, k₁ and k₂ are unstretched. Now, m is given a very slight displacement in vertical direction, what will be its time period for small vertical oscillations. k₁ = k₂ = k₃ = 6² N/m. The string that connects the left ends of k₁ and k₂ is inextensible, and is wrapped around pulley P₁ to ensure no slipping. String that connects the mass and k₃ passes over both the pulleys and does not slip over them.

A particle of mass M at rest decays into two particles of masses m₁ and m₂ having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles l₁ and l₂ is

From point A located on a highway, one has to get by car as soon as possible to point B, located in the field at a distance from the highway. It is known that the car moves in the field h times slower than on the highway. The distance from the point D one must turn off the highway i.e. distance CD is:

For a particle executing SHM, the displacement x given by x = A cos Wt. Identify the graph which represents the variation of potential energy (PE) as a function of time t and displacement x.

The half-life of ²¹⁵At is 100 ms. The time taken for the radioactivity of a sample of ²¹⁵At to decay to of its initial value is

If the area of each plate is S and the successive separations are d, 2d and 3d, then the equivalent capacitance across A and B is

A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, R is equal to

A cube of mass m and density D is suspended from a point P by a spring of stiffness k. The system is kept inside a beaker filled with a liquid of density d. The elongation in the spring, assuming D > d, is

In the shown circuit, all three capacitors are identical and have capacitance C each. Each resistor has a resistance R. An ideal cell of emf V is connected as shown. Then, the magnitude of potential difference across capacitor C₃ in steady state is

In a certain organ pipe, three successive resonance frequencies are observed at 425 Hz, 595 Hz and 765 Hz, respectively. If the speed of sound in air is 340 m/s, then the length of the pipe is

The length of a metal wire is when the tension in it is T₁, and when the tension is T₂. The natural length of the wire is

^{_{ABC is an equilateral triangle. From point A, a projectile is thrown such that it just grazes over B. Given, length of AB = . The angle of projection `` is}}

A simple pendulum of length and with a bob of mass M is at equilibrium under action of constant forces F₁ and F₂. The string makes an angle `` with the vertical and is in equilibrium. The angular frequency of oscillations of the pendulum about equilibrium position is

A weight of mass 1 kg, attached to a spring with force constant 20 N/m, is able to oscillate on a horizontal steel rod. The initial displacement from the position of equilibrium is 30 cm. If one swing is considered as the movement from maximum displacement to the equilibrium position (or) back, find how many swings will the weight make before stopping completely. Coefficient of friction between the weight and the rod is The rod is long enough. (Assume there is no surface below the weight and g = 10 m/s²)

A certain mass of an ideal diatomic gas contained in a closed vessel is heated. It is observed that the temperature remains constant, however, half the amount of gas gets dissociated. The ratio of the heat supplied to the gas to the initial internal energy of the gas will be

In the figure shown below, find out the value of . [Assume string to be tight]

The ratio of translational and rotational kinetic energies at 100 K temperature is 3 : 2. Then, the internal energy of one mole of gas at that temperature is [R = 8.3 J/mol-K]

Wires AB and PQ lie in the same vertical plane and AB remains in equilibrium due to magnetic repulsive force. Then, the time period of oscillation of the rod AB, if it is displaced by a small distance in vertical plane, will be (where PQ is fixed on a horizontal surface)

Particle A starts from rest at t = 0 from x = 0 with constant acceleration to reach x = 1 m at t = 1 s. Particle B starts with uniform velocity at t = 0 from x = 1 to reach x = 2m at t = 1 s. What will be the distance covered by particle B in the frame of reference attached to particle A from t = 0 to t = 1 s. (upto two decimal places in meter)

Two concentric shells, A and B, having radii R and 2R carry changes q_A and q_B and potential 2V and , respectively. Now, shell B is earthed and as a result, final charges on shell A and B are , respectively. Then,

A plank of mass 4m and length l is kept on a frictionless surface. A small block of mass m is kept on upper surface of the plank at point A, as shown in the figure. Coefficient of friction between the block and the plank is . What minimum velocity must be given to the block in horizontal direction so that it just comes to the other end i.e. at point B of the plank?

A rod of length L, with sides fully insulated, is made of a material whose thermal conductivity varies with temperature as K = , where is a constant. The ends of the rod are kept at temperatures T₁ and T₂. The temperature T at x, where x is the distance from the end whose temperature is T₁, is

A small water drop falls in air with terminal velocity. If R₁ and R₂ are the radii of curvature at the upper and lower points of the surface of drop, respectively and h is the distance between the two points, then (R₁ - R₂) is (approximately) [ = Density of water, T = Surface tension)