Q- An object of mass m starts from rest and slides a distance d down a frictionless incline of angle θ. While sliding, it contacts an unstressed spring of negligible massand force constant k. The object slides an additional distance x as it is brought momentarily to rest by compression of the spring. Find the initial separation d between object and spring.

### Heat and Thermodynamics

Q- 0.110 mol of a monatomic gas follows the process shown in the figure.

(a) How much heat energy is transferred to or from the gas during process 1 → 2 ?

(b) How much heat energy is transferred to or from the gas during process 2 → 3?

(c) What is the total change in thermal energy of the gas?

### Ray Optics: Achromatic Lens

Q- An achromatic doublet consists of a biconvex positive lens of refractive index μ_{1} in contact with a plano concave lens of refractive index μ_{2}. All curved surfaces have a radius of curvature R = 25 cm.

(a) If μ_{1red} = 1.49 what is the focal length of the biconvex lens for red light?

(b) If μ_{2red} = 1.54 what is the focal length of the plano convex lens for red light?

(c) What is the focal length of the doublet for red light?

(d) If μ_{1blue} = 1.52 what must be the value of μ_{2blue} for the combination to be achromatic?

### Circular Motion

A 1.9 kg ball is attached to the lower end of a length of fishline with a breaking strength of 35 N. The top end of the fishing line is held stationary. The ball is released from rest with the line taut and horizontal. At what angle (measured from the vertical) will the fishline break?

### D C Circuits

Q- Consider the circuit in the figure. The switch is closed for long time prior to t = 0.

(a) Determine the voltage V_{c} across the capacitor before t = 0 and long time after t = 0

(b) Find the expression for the voltage across the capacitor as a function of time

(c) Determine the time constant after the switch is closed

(d) Plot the voltage across capacitor for -2 < t < 5 second