A rod of length L is placed along the x-axis between x= 0 and x= L. The linear density (mass/length)$\lambda$ of the rod varies with the distance x from the origin as $\lambda$= 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.

2.

3.

4.

Concept Questions :-

Integration
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

A wheel rotates with an angular acceleration . Here t is the time and a, b are constants. If the wheel has an initial angular velocity ${\omega }_{0}$, find (a) the angular velocity and (b) the angle turned as function of time

[This question is only for Dropper and XII batch]

Concept Questions :-

Integration
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

Two discs of radii R and 2R are pressed against each other. Initially disc with radius R is rotating with angular velocity $\omega$ 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. $\omega$

2. $\omega$/2

3. $\omega$/3

4. $\frac{2\omega }{3}$

Concept Questions :-

Integration
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

The gravitational field due to a mass distribution is given by , 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. $\frac{k}{{a}^{2}}$

2. $\frac{-k}{{a}^{2}}$

3. $\frac{k}{a}$

4. $\frac{-k}{a}$

Concept Questions :-

Integration
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

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. $\frac{MgL}{AY}$

2. $\frac{MgL}{2AY}$

3. $\frac{2MgL}{AY}$

4. $\frac{3MgL}{2AY}$

Concept Questions :-

Integration
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

Consider a liquid of density $\rho$ in a container that spins with angular velocity $\omega$ 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. $y=\frac{\omega x}{2g}$

2. $y=\frac{{\omega }^{2}{x}^{2}}{2g}$

3. $y=\frac{{\omega }^{2}x}{2g}$

4. $y=\frac{\omega {x}^{2}}{2g}$

Concept Questions :-

Integration
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

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.

2.

3.

4.

Concept Questions :-

Integration
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

The specific heat of a substance varies with temperature t($°C$) as
c= 0.20 + 0.14 t + 0.023 . 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

High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

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 ${L}_{F}$= 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

Concept Questions :-

Integration
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

The temperature of n moles of an ideal gas is increased from  through a process $P=\frac{\alpha }{T}$ . Find the work done by the gas. [This question is only for Dropper and XII batch]

1. $\frac{nR{T}_{0}}{2}$

2. $nR{T}_{0}$

3. $\frac{3}{2}nR{T}_{0}$

4. 2 $nR{T}_{0}$

Concept Questions :-

Integration