### ISAT 2011 Paper

1. A projectile is fired at an angle 60◦ with some velocity u. If the angle is changed infinitesimally, let the

corresponding fractional changes in the range and the time of flight be x and y, respectively, Then y is

(A) 2/3 x

(B) −2/3 x

(C) 2x

(D) −2x

2. A ball is dropped down vertically from a tall building. After falling a height h it bounces elastically from a table inclined at an angle θ and hits a wall at a distance d from the point of earlier impact horizontally, then

(A) θ = (1/2) sin^{−1}(2d/h)

(B) θ = (1/2) tan^{−1}(d/h)

(C) θ = (1/4) sin^{−1}(d/h)

(D) θ = (1/2) tan^{−1}(2d/h)

3. A photon with an initial frequency 1011Hz scatters off an electron at rest. Its final frequency is

0.9×10^{11} Hz. The speed of the scattered electron is close to (h = 6.63×10^{−34} Js, me = 9.1×10^{−31} kg)

(A) 4 × 10^{3} ms^{−1}

(B) 3 × 10^{2}−1

(C) 2 × 10^{6}−1

(D) 30ms^{−1}

4. The central fringe in a Young’s double slit experiment with the He-Ne laser (λ = 632.8 nm) has intensity I0. If one of the slits is covered by a 5μm thick film of plastic (refractive index = 1.4), the intensity becomes I_{1}. The ratio I_{1}/I_{o} is close to

(A) 3/16

(B) 1/4

(C) 1/2

(D) 3/4

5.A submarine traveling at 10 ms−1 is chasing another one in front of it. It locates its position and speed by sending Sonar (ultrasonic sound) towards it and recording the time of its travel and return frequency. The frequency of the Sonar is 25000 Hz and the frequency of the reflected signal is 24900 Hz. If the speed of sound in water is 1500 ms−1, the speed of the submarine being chased is

(A) 16 ms^{−1}

(B) 14 ms^{−1}

(C) 13 ms^{−1}

(D) 11 ms^{−1}

6.Laplace correction to the speed of sound is made only for gases and not for solids and liquids. This is because, in comparison to gases, liquids and solids have

(A) larger thermal conductivity

(B) much smaller compressibility

(C) much smaller coefficient of thermal expansion

(D) much smaller relative pressure change when the wave is passing through the

7.In an experiment designed to determine the universal gravitational constant, G, the percentage errors in measuring the appropriate mass, length and time variables are given by a, b, c respectively. The total error in determining G is then

(A) (a + 3b + 2c)

(B) (−a + 3b − 2c)

(C) (2a + 3b + 2c)

(D) (a + 9b + 4c)

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