A galvanometer having a resistance of 20 $$\Omega$$ and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is:

In the circuit shown, the potential difference between A and B is :

In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A. If a 10 $$\Omega$$ resistor is connected in series with R1, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R1 + 10) $$\Omega$$ such that the null point shifts back to its initial position is :

The galvanometer deflection, when key K1 is closed but K2 is open, equals $$\theta$$0 (see figure). On closing K2 also and adjusting R2 to 5$$\Omega$$, the deflection in galvanometer becomes {{{\theta _0}} \over 5}. . The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery] :

An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and esistance 5 $$\Omega$$. The value of R, to give a potential difference of 5 mV across 10 cm of potentiometer wire, is :

The Wheatstone bridge shown in figure, here, gets balanced when the carbon resistor used as R1 has the colour code (Orange, Red, Brown). The resistors R2 and R4 are 80$$\Omega$$ and 40$$\Omega$$, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as R3, would be -

A body of mass 2 kg makes an eleastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body ?

Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be :

A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 ms–1 with respect to the man. The speed of the man with respect to the surface is :

Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds u1 and u2, respectively. The values of u1 and u2 are nearly :

A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by :-

A particle of mass 'm' is moving with speed '2v' and collides with a mass '2m' moving with speed 'v' in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass 'm', which move at angle 45° with respect to the origianl direction. The speed of each of the moving particle will be :-

A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height (p-h) diagram is :

A body of mass m1 moving with an unknown velocity of $$v_1\stackrel{\wedge }{i}$$, undergoes a collinear collision with a body of mass m2 moving with a velocity $$v_2\stackrel{\wedge }{i}$$ . After collision, m1 and m2 move with velocities of $$v_3\stackrel{\wedge }{i}$$ and $$v_4\stackrel{\wedge }{i}$$ , respectively. If m2 = 0.5 m1 and v3 = 0.5 v1, then v1 is :-

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :-

Four particles A, B, C and D with masses mA = m, mB = 2m, mC = 3m and mD = 4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is :

If 1022 gas molecules each of mass 10–26 kg collide with a surface (perpendicular to it) elastically per second over an area 1 m2 with a speed 104 m/s, the pressure exerted by the gas molecules will be of the order of :

Two masses m and {m \over 2} are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k, at the centre of mass of the rod-mass system(see figure). Because of torsional constant k, the restoring torque is $$\tau$$ = k$$\theta$$ for angular displacement $$\theta$$. If the rod is rotated by $$\theta$$0 and released, the tension in it when it passes through its mean position will be :

Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M, Block A is given an initial speed $$\upsilon$$ towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically {5 \over 6}th of the initial kinetic energy is lost in whole process. What is value of M/m ?

A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms–1, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is - (g = 10 ms–2)