JEE Advanced 2014 — Set 2

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy 𝐾𝐾 with time𝑡𝑡 most appropriately? The figures are only illustrative and not to the scale.

A wire, whichpasses through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

During an experiment with ametre bridge, the galvanometer shows a null point when the jockey is pressed at 40.0 𝑐𝑐𝑚𝑚 using a standard resistance of 90 𝛺𝛺,as shown in the figure. The least count of the scale used in the metre bridge is1 𝑚𝑚𝑚𝑚. The unknown resistance is

Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R, respectively, as shown in figure. If magnitudes of the electric fields at point P at a distance R from the center of spheres 1, 2 and 3 are E1, E2 and E3respectively, then

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is

Parallel rays of light of intensity 𝐼𝐼= 912 𝑊𝑊𝑚𝑚−2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant 𝜎𝜎= 5.7 × 10−8𝑊𝑊𝑚𝑚−2𝐾𝐾−4 and assume that the energy exchange with the surroundingsis only through radiation. The final steady state temperature of the black body is close to

A metal surface is illuminated by light of two different wavelengths 248nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths areu1 and u2,respectively. If the ratio 𝑢𝑢1: 𝑢𝑢2 = 2: 1and hc = 1240 eV nm, the work function of the metal is nearly

If 𝜆𝜆𝐶𝐶𝐶𝐶 is the wavelength of 𝐾𝐾𝛼𝛼X-ray line of copper (atomic number 29) and 𝜆𝜆𝑀𝑀𝑀𝑀 is the wavelength of the 𝐾𝐾𝛼𝛼X-ray line of molybdenum (atomic number 42), then the ratio 𝜆𝜆𝐶𝐶𝐶𝐶/𝜆𝜆𝑀𝑀𝑀𝑀 is close to

A planet of radius 𝑅𝑅= 1 10 × (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth 𝑅𝑅 5on it and lower a wire of the same length and of linear mass density 10−3𝑘𝑘𝑘𝑘𝑚𝑚−1 into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth = 6 × 106𝑚𝑚 and the acceleration due to gravity on Earth is 10 ms ̶ 2)

A glass capillary tube is of the shape of a truncated cone with an apex angle 𝛼𝛼so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cross section is 𝑏𝑏. If the surface tension of water is S, its density is ρ, and its contact angle with glass is 𝜃𝜃, the value of h will be (g is the acceleration due to gravity)