ToppersNotes

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Q.1 Two point masses of 0.3kg and 0.7kg are fixed at the ends of a rod which is of length 1.4m

and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a

uniform angular speed. The point on the rod through which the axis should pass in order that

the work required for rotation of the rod is minimum is located at a distance of?

(A) 0.42 from the mass of 0.3kg (B) 0.70 m from the mass of 0.7kg

(C) 0.98m from the mass of 0.3kg (D) 0.98m from the mass of 0.7kg

Q.2 A mass m moving with a constant velocity along a line parallel to the x axis, away from the origin. Its angular momentum with respect to the origin. (A) is zero (B) remains constant (C) goes on increasing (D) goes on decreasing Q.3 Water is filled in a container upto height 3m. A small hole of area 'a' is punched in the wall of the container at a height 52.5 cm from the bottom. The cross sectional area of the container is A. If a/A=0.1 then v2 is (where v is the velocity of water coming out of the hole)? (A) 48 (B) 51 (C) 50 (D) 51.5 Q. 4 Water from a tap emerges vertically downwards with an initial speed of 1.0 ms-1. The cross−sectional area of the tap is 10-4 m2. Assume that the pressure is constant throughout the stream of water, and that the flow is steady. The cross−sectional area of the stream 0.15 m below the tap is? (A) 5.0 × 10−4 m2 (B) 1.0 ×10−5 m2 (C) 5.0 × 10−5 m2 (D) 2.0 × 10−5 m2

Q.5 Two particles, each of mass m & charge q, are attached to the two ends of a light rigid rod of length 2R.The rod is rotated at constant angular speed about a perpendicular axis passing through its centre.The ratio of the magnitudes of the magnetic moment of the system & its angular momentum about the centre of the rod is ?

(A) q/2m (B) q/m (C)2q/m (D)q/ pm

Q.6 A battery is connected between two points A and B the circumference of a uniform conducting ring of radius r and resistance R . One of the arcs AB of the ring subtends an angle q at the centre. The value of the magnetic induction at the centre due to the current in the ring is : (A) zero , only if q = 180º (B) zero, for all values of q (C) proportional to 2 (180º - q) (D) inversely proportional to r Q.7 A charged particle having mass m and charge q is accelerated by a potential difference V, it flies through a uniform transverse magnetic field B. The field occupies a region of space d. Find the time interval for which it remains inside the magnetic field? Q.8 A charged particle (charge q, mass m) has velocity v0 at origin in +x direction. In space there is a uniform magnetic field B in - z direction. Find the y coordinate of particle when is crosses y axis? Q.9 A diwali cracker known as sudarashan chakra works on the principle of thrust.Consider such a toy the centre of which is hinged.The initial mass of the toy is M0 and radius is R . The toy is in the shape of a spiral the turns of which are very close (it can be assumed as a disc).The gases are ejected tangentially from the end of the toy with a constant velocity u relative to the toy. Find the angular velocity of the toy when mass remains half. Q. 10 A uniform ball of radius R rolls without slipping between two rails such that the horizontal distance is d between two contact points of the rail to the ball. If R=10cm, d=16cm and the angular velocity is 5rad/s then find the velocity of centre of mass of the ball. Q.11 Two arms of a U-tube have unequal diameters d1= 1.0 mm and d2 = 1.0 cm. If water (surface tension 7 × 10-2 N/m) is poured into the tube held in the vertical position, find the difference of level of water in the U-tube. Assume the angle of contact to be zero. Q.12 A wooden stick of length l, and radius R and density r has a small metal piece of mass m (of negligible volume) attached to its one end. Find the minimum value for the mass m (in terms of given parameters)that would make the stick float vertically in equilibrium in a liquid of density s (>r)?