If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :

A student determined Young's Modulus of elasticity using the formula Y = {{Mg{L^3}} \over {4b{d^3}\delta }}. The value of g is taken to be 9.8 m/s2, without any significant error, his observation are as following. .tg {border-collapse:collapse;border-spacing:0;width:100%} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-baqh{text-align:center;vertical-align:top} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} Physical Quantity Least count of the Equipment used for measurement Observed value Mass (M) 1 g 2 kg Length of bar (L) 1 mm 1 m Breadth of bar (b) 0.1 mm 4 cm Thickness of bar (d) 0.01 mm 0.4 cm Depression ($$\delta$$) 0.01 mm 5 mm Then the fractional error in the measurement of Y is :

The focal length f is related to the radius of curvature r of the spherical convex mirror by :

A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value | f | = 40 cm. The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may conclude from the information :

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $$\overrightarrow{a}$$, $$\overrightarrow{b}$$ and $$\overrightarrow{c}$$ respectively. Then choose the correct relation for these vectors.

Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R. Assertion A : For a simple microscope, the angular size of the object equals the angular size of the image. Reason R : Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below :

The angle of deviation through a prism is minimum when (A) Incident ray and emergent ray are symmetric to the prism. (B) The refracted ray inside the prism becomes parallel to its base (C) Angle of incidence is equal to that of the angle of emergence (D) When angle of emergence is double the angle of incidence Choose the correct answer from the options given below :

The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index? Assume the radii of curvature of the faces of lens are R1 and R2 respectively.

Red light differs from blue light as they have :

The thickness at the centre of a plane convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 $$\times$$ 108 ms$$-$$1. The focal length of the lens is ____________.

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as :

Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in the figure. The refractive indices of the material of the prism for red, green and blue wavelength are 1.27, 1.42 and 1.49 respectively. The colour of the ray(s) emerging out of the face PR is :

Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is :

A ray of light passes from a denser medium to a rarer medium at an angle of incidence i. The reflected and refracted rays make an angle of 90$${}^{\circ }$$ with each other. The angle of reflection and refraction are respectively r and r'. The critical angle is given by

A ray of laser of a wavelength 630 nm is incident at an angle of 30$${}^{\circ }$$ at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is 2.42 and that of air is 1. Choose the correct option.

A prism of refractive index $$\mu$$ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in terms of refractive index

A ray of light entering from air into a denser medium of refractive index {4 \over 3}, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $$\theta$$ should be equal to :

The expected graphical representation of the variation of angle of deviation '$$\delta$$' with angle of incidence 'i' in a prism is :

Car B overtakes another car A at a relative speed of 40 ms$$-$$1. How fast will the image of car B appear to move in the mirror of focal length 10 cm fitted in car A, when the car B is 1.9 m away from the car A?

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is d1 from C and the distance of the image formed is d2 from C, the radius of curvature of this mirror is :