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A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed ω, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains ω throughout. The magnitude of the torque (|t|) on the system about O, as a function of time is best represented by which plot ?
Answer figuers

A 1
B 2
C 3
D 4

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is

A 1
B 2
C 3
D 4

Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field JEE_IIT_2012_question_paper_with_answer_on_testveda_test_veda_q3 and the electric potential V(r) with the distance r from the centre, is best represented by which graph ?

A 1
B 2
C 3
D 4

In the determination of Young's modulus JEE_IIT_2012_question_paper_with_answer_on_testveda_test_veda_q4 by using Searle's method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load m= 2.5 kg, an extension l= 0.25 mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement.

A due to the errors in the measurements of d and l are the same.
B due to the error in the measurement of d is twice that due to the error in the measurement of l
C due to the error in the measurement of l is twice that due to the error in the measurement of d
D due to the error in the measurement of d is four times that due to the error in the measurement of l

A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at  t= 0. It then executes simple harmonic motion with angular frequency ω = π/3 rad/s. Simultaneously at t= 0, a small pebble is projected with speed v from point p at an angle of 45° as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1 s, the value of v is (take g =10 m/s2)

A √50 m/s
B √51 m/s
C √52 m/s
D √53 m/s

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