Instructions

For the following questions answer them individually

Question 11

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?

Question 12

Two identical moving coil galvanometers have $$10 Î©$$ resistance and full scale deflection at $$2 \mu A$$ current. One of them is converted into a voltmeter of 100 m V full scale reading and the other into an Ammeter of 1mA full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohmâ€™s law experiment with $$R = 1000 Î©$$ resistor by using an ideal cell. Which of the following statement(s) is/are correct?

Question 13

A particle is moved along a path AB-BC-CD-DE-EF-FA, as shownin figure, in presence of a force $$\overrightarrow{F} = (\alpha y\widehat{l} + 2\alpha x\widehat{j}) N$$, where x and y are in meter and $$\alpha = -1 Nm^{-1}$$. The work done on the particle by this force $$\overrightarrow{F}$$ will be ___ Joule.

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Question 14

A block of weight 100 N is suspended by copper and steel wires of same cross sectional area $$0.5 cm^2$$ and, length $$\sqrt 3 m$$ and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copperand steel wires with ceiling are $$30^\circ and 60^\circ$$, respectively. If elongation in copper wire is $$(\triangle l_C)$$ and elongation in steel wire is $$(\triangle l_S)$$, then the ratio $$\frac{\triangle l_C}{\triangle l_S}$$ is.

[Youngâ€™s modulus for copper andsteel are $$1 \times 10^{11} N/m^2 and 2 \times 10^{11} N/m^2$$, respectively.]

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Question 15

A tram S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is __________.

[Speed of the sound = 330 m/s]

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Question 16

A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness $$\delta = \frac{d}{N}$$. The dielectric constant of the $$m^{th}$$ layer is $$K_m = K \left(1 + \frac {m}{N}\right)$$, For a very large $$N (> 10^3)$$, the capacitance C is $$\alpha \left(\frac{K \epsilon_0A}{d ln 2}\right)$$. The value of $$\alpha$$ will be _________.

[$$\epsilon_0$$ is the permittivity of free space]

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Question 17

A liquid at $$30^\circ C$$ is poured very slowly into a Calorimeter that is at temperature of $$110^\circ C$$ . The boiling temperature of the liquid is $$80^\circ C$$ . It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is found to be $$50^\circ C$$ . The ratio of the Latent heat of the liquid to its specific heat will be $$^\circ C$$

[Neglect the heat exchange with surrounding]

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Question 18

A planar structure of length Â£ and width W is made of two different optical media of refractive indices $$n_1 = 1.5 and n_2 = 1.44$$ as shown in figure. If $$L \gg W$$, a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure. For L = 9.6 m, if the incident angle $$\theta$$ is varied, the maximum time taken by array to exit the plane CD is $$t \times 10^{-9} s$$, where t is _______.

[ Speed of light $$c = 3 \times 10^8 m/s$$]

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