A galvanometer having a coil resistance 100 $$\Omega$$ gives a full scale deflection when a current of 1 mA is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter giving full scale deflection for a potential difference of 10 V?

In the given circuit diagram, a wire is joining points B and D. The current in this wire is :

Particle A of mass m1 moving with velocity $$\left(\sqrt{3}\hat{i}+\hat{j}\right)m{s}^{-1}$$ collides with another particle B of mass m2 which is at rest initially. Let $$\overrightarrow{V_1}$$ and $$\overrightarrow{V_2}$$ be the velocities of particles A and B after collision respectively. If m1 = 2m2 and after collision $$\overrightarrow{V_1}=$$$$\left(\hat{i}+\sqrt{3}\hat{j}\right)$$ , the angle between $$\overrightarrow{V_1}$$ and $$\overrightarrow{V_2}$$ is :

Blocks of masses m, 2m, 4m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m starts moving the total energy loss is p% of the original energy. Value of 'p' is close to :

A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10 m/s2 . Assume there is no rotational motion and loss of energy after the collision is negligable.]

Two particles of equal mass m have respective initial velocities $$u\hat{i}$$ and u\left( {{{\widehat i + \widehat j} \over 2}} \right). They collide completely inelastically. The energy lost in the process is :

A block of mass m = 1 kg slides with velocity v = 6 m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle $$\theta$$ before momentarily coming to rest. If the rod has mass M = 2 kg, and length $$l$$ = 1 m, the value of $$\theta$$ is approximately : (take g = 10 m/s2)

A particle of mass m with an initial velocity $$u\hat{i}$$ collides perfectly elastically with a mass 3 m at rest. It moves with a velocity $$v\hat{j}$$ after collision, then, v is given by :

A particle of mass m is projected with a speed u from the ground at an angle \theta = {\pi \over 3} w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $$u\hat{i}$$ . The horizontal distance covered by the combined mass before reaching the ground is:

A rod of length L has non-uniform linear mass density given by $$\rho$$(x) = a + b{\left( {{x \over L}} \right)^2} , where a and b are constants and 0 $$\le$$ x $$\le$$ L. The value of x for the centre of mass of the rod is at :

A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $$\sqrt{2gh}$$. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of \sqrt {{h \over g}} is :

As shown in figure, when a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (centered at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e, on the surface of the cavity. R can be detemined by the equation :

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are :

Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at a point:

A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms–1 at a point where the pressure is P pascal. At another point where pressure is {P \over 2} Pascal its speed is V ms–1. If the density of the fluid is $$\rho$$ kg m–3 and the flow is streamline, then V is equal to :

An object of mass m is suspended at the end of a massless wire of length L and area of crosssection A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :

In an experiment to verify Stokes law, a small spherical ball of radius r and density $$\rho$$ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to : (ignore viscosity of air)

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is {{27} \over 8} w.r.t water, the value of r is :

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x1 and in the other, x2 . When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:

A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, B = 8 $$\times$$ 1010 Pa)