The relationship between force and position is shown in the figure given (in one dimensional case). Find the work done by the force in displaying a body from x= 1 cm to x= 5cm is [This question includes concepts from Work, Energy and Power chapter]

1. 10 erg

2. 20 erg

3. 30 erg

4. 40 erg

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.  

1. 10 U

2. 15 U

3. 20 U

4. 25 U

A spring of spring constant $5\times {10}^3 N/m$ is stretched initially by 5 cm from the unstretched position. Find the work required to stretch it further by another 5 cm is   -

1. 15 J

2. 18.75 N .m

3. 20 J

4. 22.75 N .m

A constant force F is applied on a body. The power (P) generated is related to the time elapsed (t) as [This question includes concepts from Work, Energy and Power chapter]

1. $P \propto t^2$

2. $P \propto t$

3. $P \propto \sqrt{ t}$

4. $P \propto t^{3/2}$

The gravitational field due to a mass distribution is given by $\overrightarrow{I}= \frac{k}{x^2}\hat{i}$, where k is a constant. Assuming the potential to be zero at infinity, find the potential at a point x = a.[This question includes concepts from Gravitation chapter]

1. $\frac{k}{a^2}$

2. $\frac{-k}{a^2}$

3. $\frac{k}{a}$

4. $\frac{-k}{a}$

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. $y=\frac{\omega x^2}{2g}$

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. ${10}^4 Nm$

2. $2\times {10}^4 Nm$

3. $3\times {10}^4 Nm$

4. $4\times {10}^4 Nm$

The specific heat of a substance varies with temperature t($°C$) as
c= 0.20 + 0.14 t + 0.023 $t^2 (cal/gm °C)$. 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

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

The temperature of n moles of an ideal gas is increased from $T_0 to 2T_0$ 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 $nR{T}_0$