The upper edge of a gate in a dam runs along water surface. The gate is 2 m high and 3 m wide and is hinged along a horizontal line through its center. Calculate the torque about hinge. [This question is only for Dropper and XII batch]

1. 104 Nm

2. 2×104 Nm

3. 3×104 Nm

4. 4×104 Nm

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The specific heat of a substance varies with temperature t(°C) as
c= 0.20 + 0.14 t + 0.023 t2 (cal/gm °C). Find the heat required to raise the temperature of 2 gm of substance from 5°C to 15 °C[This question is only for Dropper and XII batch]

1. 41 cal

2. 82 cal

3. 80 cal

4. 40 cal

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An isolated container at 127°C contains an ice cube of mass 100 g at 0°C. The specific heat C of container varies with temperature according to relation C= a+bT, where a= 0.1 kcal/kg-K and b= 40 m cal/kg K. Find the mass of container, if the final temperature of container is 300 K.
[Take LF= 80 cal/g and specific heat of water 1 cal/g K]

[This question is only for Dropper and XII batch]

1. 500 g

2. 720 g

3. 940 g

4. 1200 g

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The temperature of n moles of an ideal gas is increased from T0 to 2T0 through a process P=αT . Find the work done by the gas. [This question is only for Dropper and XII batch]

1. nRT02

2. nRT0

3. 32nRT0

4. 2 nRT0

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Electric field is given by E =100x2 . Find the potential difference between x= 10 and x= 20 m. [This question is only for Dropper and XII batch]

1. 5 V

2. 10 V

3. 15 V

4. 20 V

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Calculate the electric field on the axis of a very long uniformly charged, thin rod at a distance r from one end. The charge per unit length of the rod is λ[This question is only for Dropper and XII batch]

1. 2kλr

2. kλr

3. kλ2r

4. kλ4r

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Find electric field at the centre of arc which subtends 'θ' angle at centre

[This question is only for Dropper and XII batch]

1. 2kλrsin θ

2. 2kλrsinθ4

3. 2kλrsinθ2

4. 2kλrsin2θ

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Find electric field due to a uniformly charged, long and thin rod

[This question is only for Dropper and XII batch]

1. kλr

2. kλ2r

3. 2kλr

4. kλ4r

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A ball of radius R carries a positive charge throughout its volume, such that the volume density of charge depends on distance r from the ball's centre as ρ=ρ01-rR, where ρ0 is a constant. Assuming the permittivity of ball to be one, find magnitude of electric field as a function of distance r, both inside  the ball. [This question is only for Dropper and XII batch]

1.ρ0r3ε0

2. ρ0(4rR-3r2)12ε0R 

3. ρ0(4rR-3r2)3ε0R

4. ρ0(4rR-5r2)3ε0R

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The electric field vector in a region given by E=(3i^+4yj^)Vm-1. Calculate the potential at (1m, 1m) taking potential at origin to be zero. [This question is only for Dropper and XII batch]

1. 5V

2. 3V

3. -1V

4. -5V

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