A constant force F is applied on a body. The power (P) generated is related to the time elapsed (t) as

                                                                   [This question is only for Dropper and XII batch]

1. P  t2

2. P  t

3. P  t

4. P  t3/2

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A rod of length L is placed along the x-axis between x= 0 and x= L. The linear density (mass/length)λ of the rod varies with the distance x from the origin as λ= Rx. Here, R is a positive constant. Find the position of centre of mass of this rod. 

   [This question is only for Dropper and XII batch]

 

1. 0, 2L3, 0

2. 0, 0, 2L3

3. 2L3, 0, 0

4. L3, 0, 0

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A wheel rotates with an angular acceleration α= 4at3-3bt2. Here t is the time and a, b are constants. If the wheel has an initial angular velocity ω0, find (a) the angular velocity and (b) the angle turned as function of time 

   [This question is only for Dropper and XII batch]

 

 1.  w=at4-bt2+ω0     θ=at55- at44+ω0t

2.  w=at4-bt3+ω0     θ=at55- bt44+ω0t

3.  w=at3-bt2+ω0     θ=at44- at33+ω0t

4.  w=at3-bt2+ω0     θ=at44- at33+ω0t

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Two discs of radii R and 2R are pressed against each other. Initially disc with radius R is rotating with angular velocity ω and other disc was stationary. Both disc are hinged at their respective centres and free to rotate about them.Moment of inertia of smaller is I and bigger disc is 2I about their respective axis of rotation. Find the angular velocity of the bigger disc after long time. 

   [This question is only for Dropper and XII batch]

 

                     

1. ω

2. ω/2

3. ω/3

4. 2ω3

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The gravitational field due to a mass distribution is given by I= kx2i^, where k is a constant. Assuming the potential to be zero at infinity, find the potential at a point x = a. [This question is only for Dropper and XII batch]

1. ka2

2. -ka2

3. ka

4. -ka

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A bar of mass M and length L is hanging from point S as shown in figure. The Young's modulus of elasticity of the wire is Y and the area of cross-section of the wire is A. Find total elongation in bar.

[This question is only for Dropper and XII batch]

                                           

1. MgLAY

2. MgL2AY

3. 2MgLAY

4. 3MgL2AY

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Consider a liquid of density ρ in a container that spins with angular velocity ω as shown in figure. Find relation between y and x for any point P, if liquid rises due to rotation. [This question is only for Dropper and XII batch]

1. y=ωx2g

2. y=ω2x22g

3. y=ω2x2g

4. y=ωx22g

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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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