PE Diagram

Q. Given in Fig. 6.11 are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any, in which the particle cannot be found for the given energy. Also, indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.

Q.

Fig. Shows a plot of the conservation force F in a unidimensional field. The plot representing the function corresponding to the potential energy (U) in the fields is

1. 

2. 

3. 

4. 

Q. Potential energy of a particle is given by $U=(2-3x-4x^2)\text{J}$ where '$x$' is in '$m$'. Find the magnitude of force at $x=4\text{m}$, if the particle is free to move along $x$-direction.

1. $29\text{N}$
2. $35\text{N}$
3. $16\text{N}$
4. $18\text{N}$

Q. A particle is acted by a force F = kx, where k is a positive constant. Its potential energy at x = 0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x

1. 
2. 
3. 
4. 

Q. A potential energy function for a two dimensional force is of the form $U=9x^{3}y-12x$. Find conservative force at point (1, 2).

1. $-42\hat{i}-9\hat{j}$
2. $-36\hat{i}+18\hat{j}$
3. $-18\hat{i}+9\hat{j}$
4. None

Q. The potential energy for a force field $\overrightarrow{F}$ is given by $U(x,y)=\sin (x+y)$. The force acting on the particle of mass $m$ at $(0,\frac{\pi }{4})$ is (in $N$)

1. $1$
2. $2$
3. $3$
4. $4$