JEE (Advanced) 2009 Paper-1
For the following questions answer them individually
A block of base 10 cm $$\times$$ 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is $$\sqrt{3}$$. The inclination $$\theta$$ of this inclined plane from the horizontal plane is gradually increased from $$0^\circ$$. Then
The x-t graph of a particle undergoing simple harmonic is shown below. The acceleration of the particle at $$t = \frac{4}{3}s$$ is-
Three concentric metallic spherical shells of radii R, 2R, 3R are given charges $$Q_1, Q_2, Q_3$$ respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, $$Q_1 : Q_2 : Q_3$$ is-
A disk of radius $$\frac{a}{4}$$ having a uniformly distributed charge 6C is placed in the x-y plane with its centre at $$\left(\frac{-a}{2}, 0, 0\right)$$. A rod of length 'a' carrying a uniformly distributed charge 8C is placed on the x-axis from $$x = \frac{a}{4}$$ to $$x = \frac{5a}{4} $$. Two point charges -7C and 3C are placed at $$\left(\frac{a}{4}, \frac{-a}{4}, 0 \right)$$ and $$\left(\frac{-3a}{4}, \frac{3a}{4}, 0 \right)$$ respectively. Consider a cubical surface formed by six surfaces $$x = \pm \frac{a}{2}, y = \pm \frac{a}{2}, z = \pm \frac{a}{2}$$. The electric flux this cubical surface is-
Look at the drawing given in the figure which has been drawn with ink of uniform linethickness. The mass of ink used to draw each of the two inner circles, and each of the two lines segments is m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are : outer circle (0, 0), left inner circle (-a, a), right inner circle (a, a), vertical line (0, 0) and horizontal line (0, -a). The y-coordinate of the centre of mass of the ink in this drawing is-
The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. I1 and I2 are the currents in the segments ab and cd. Then
A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is $$\frac{4}{3}$$. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many collisions, other than that at A, these two particles will again reach the point A ?
If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that
