A wheel of radius 8 units rolls along the diameter of a semicircle of radius 25 units; it bumps into this semicircle. What is the length of the portion of the diameter that cannot be touched by the wheel? (a)12        (b)  15    (c)  17       (d)  20

A right triangle is drawn in a semicircle of radius 1/2 with one of its legs along the diameter. If the maximum area of the triangle is M , then the value of 32sqrt(3)M c is______

Line segments A C and B D are diameters of the circle of radius one. If /_B D C=60^0 , the length of line segment A B is_________

One angle of an isosceles triangle is 120^0 and the radius of its incircle is sqrt(3)dot Then the area of the triangle in sq. units is (a) 7+12sqrt(3) (b) 12-7sqrt(3) (c) 12+7sqrt(3) (d) 4pi

The largest area of the trapezium inscribed in a semi-circle or radius R , if the lower base is on the diameter, is (a) (3sqrt(3))/4R^2 (b) (sqrt(3))/2R^2 (c) (3sqrt(3))/8R^2 (d) R^2

In a triangle A B C , right angled at A , on the leg A C as diameter, a semicircle is described. If a chord joins A with the point of intersection D of the hypotenuse and the semicircle, then the length of A C is equal to (a) (A B.A D)/(sqrt(A B^2+A D^2)) (b) (A B.A D)/(A B+A D) (c) sqrt(A B.A D) (d) (A B.A D)/(sqrt(A B^2-A D^2))

6.A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 2.0 cm as shown in Fig. (a). Consider the magnetic field B at the centre of the arc. a . What is the magnetic field due to the straight segments? b. In what way the contribution to B from the semicircle differs from that of a circular loop and in what way does it resemble? c. Would your answer be different if the wire were bent into a semi-circular arc of the same radius but in the opposite way as shown in Fig. (b)?

Tangents are drawn from external point P(6,8) to the circle x^2+y^2 =r^2 find the radius r of the circle such that area of triangle formed by the tangents and chord of contact is maximum is (A) 25 (B) 15 (C) 5 (D) none of these

AB is a chord of x^2 + y^2 = 4 and P(1, 1) trisects AB. Then the length of the chord AB is (a) 1.5 units (c) 2.5 units (b) 2 units (d) 3 units

An electric field is uniform and in the positive xdirection for positivex and uniform with the same magnitude but in the negative x direction for negative x. It is given that E= 200 hati N//C" for "x gt 0 and E=- 200 hati N//C" for "3 lt 0. A right circular cylinder of length 20 cm and radius 5 cm has its centre at the origin and its axis along the x-axis so that one tace is at x = +10 em and the other is at x=10 cm a. What is the net outward flux through cach flat face? b. What is the flux through the side of the cylinder? c. What is the net outward flux through the cylinder?

A 100 turn closely wound circular coil of radius 10 cm carries a current of 3.2 A. a. What is the field at the centre of the coil ? b. What is the magnetic moment of this coil ? The coil is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter. A unifrom magnetic field of 2 T in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of 90^@ under the influence of the magnetic field . c. What are the magnitudes of the torques on the coil in the initial and final position ? d. What is the angular speed acqired by the coil when it has rotated by 90^(@) ? The moment of inertia of the coil is 0.1 kg m^2