A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as Fx=-kx + ax3. Here k and a are positive constants. For x0, the functional form of the potential energy Ux of the particle is

 [This question is only for Dropper and XII batch]

1. 

2. 

3. 

4. 

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A long spring is stretched by 2 cm, its potential energy is U. If the spring is streched by 10 cm, find the potential energy stored in it.   [This question is only for Dropper and XII batch]

1. 10 U

2. 15 U

3. 20 U

4. 25 U

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A spring of spring constant 5×103 N/m is stretched initially by 5 cm from the unstretched position. Find the work required to stretch it further by another 5 cm is   [This question is only for Dropper and XII batch]

1. 15 J

2. 18.75 N .m

3. 20 J

4. 22.75 N .m

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An automobile of mass m accelerates, starting from rest, while the engine supplies constant power P, its position and velocity changes w.r.t time as-    [This question is only for Dropper and XII batch]

1. Pt9m12 t1/2, 2Ptm12

2. 2Pt9m12 t3/2, Ptm12

3. 8P9m12t3/2, 2Ptm12

4. 8P9m12t3/2, Ptm32

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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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