Practice Questions

Q1. The time period of a simple pendulum is given by T = 2π√lg pendulum is 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of g using this pendulum is x. The value of x to the nearest integer is:- (1) 2% (2) 3% (3) 5% (4) 4%

Q1. Statement I: If three forces →𝐹1, →𝐹2 and →𝐹3 are represented by three sides of a triangle and →𝐹1 + →𝐹2 = - →𝐹3, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement II: A triangle made up of three forces →𝐹1, →𝐹2 and →𝐹3 as its sides were taken in the same order, satisfies the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below: (1) Both Statement I and Statement II are true. (2) Statement I is true but Statement II is false. (3) Both Statement I and Statement II are false. (4) Statement I is false but Statement II is true.

Q1. The period of oscillation of a simple pendulum is T = 2π√Lg having a minimum division of 1 mm and time of one complete oscillation is 1. 95 s measured from stopwatch of 0. 01 s resolution. The percentage error in the determination of ′g′ will be: (1) 1. 03% (2) 1. 33% (3) 1. 30% (4) 1. 13%

Q1. If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity hc 4πε0 has dimensions of : (1) [MLT0] (2) [M0 L0 T0] (3) [MLT−1] (4) [LC−1]

Q1. The work done by a gas molecule in an isolated system is given by, 𝑊= 𝛼𝛽2𝑒- 𝛼𝑘 𝑇, where 𝑥 is the displacement, 𝑘 is the Boltzmann constant and 𝑇 is the temperature. 𝛼 and 𝛽 are constants. Then the dimensions of 𝛽 will be: (1) M2 L T2 (2) ML2 T-2 (3) MLT-2 (4) M0 L T0

Q1. A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t seconds, the total distance travelled is: (1) (α+β) 4αβ t2 (2) (α+β)2αβ t2 (3) 2(α+β) αβ t2 (4) 4(α+β)αβ t2

Q2. A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is: (1) 0. 0314 N (2) 9. 859 × 10−2 N (3) 6. 28 × 10−3 N (4) 9. 859 × 10−4 N

Q2. The angle between vector and A − is : (A) ( B) (1) tan−1( A−BB cossinθ θ ) (2) tan−1( 2√3A−BB ) √3 (3) tan−1( A−B−B2 (4) tan−1( 0.7BA ) 2 )

Q2. A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is : (1) 25 m (2) 45 m (3) 35 m (4) 50 m

Q2. Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring constant K . A third block C of mass m moving with a speed v along the line joining A and B collides with A.The maximum compression in the spring is (1) v√m2K (2) √mv2K (3) √mvK (4) √m2K

Q2. Statement-I : Two forces →𝑃+ →𝑄 and →𝑃- →𝑄 where →𝑃⊥→𝑄, when act at an angle 𝜃1 each other, the magnitude of their resultant is √3𝑃2 + 𝑄2, when they act at an angle 𝜃2, the magnitude of their resultant becomes √2𝑃2 + 𝑄2 . This is possible only when 𝜃1 < 𝜃2 . Statement-II : In the situation given above. 𝜃1 = 60° and 𝜃2 = 90° In the light of the above statement, choose the most appropriate answer from the options given below : (1) Statement I is false but Statement II is true. (2) Both Statement I and Statement II are true. (3) Both Statement I and Statement II are false. (4) Statement I is true but Statement II is false.

Q2. If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is: (1) [t−1v1l−2] (2) [t1v2l−1] (3) [t−2v−1l1] (4) [t−1v−2l1]

Q2. A bullet of 4 g mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms1, the impulse imparted to the gun and velocity of recoil of gun are (1) 0. 4 kg m s−1, 0. 1 m s−1 (2) 0. 2 kg m s−1, 0. 05 m s−1 (3) 0. 2 kg m s−1, 0. 1 m s−1 (4) 0. 4 kg m s−1, 0. 05 m s−1

Q2. Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th second after its fall to the next droplet is 34 . 3 m. At what rate the droplets are coming from the tap ? (Take 𝑔= 9 . 8 m s-2) (1) 3 drops/2 seconds (2) 2 drops/second (3) 1 drop/second (4) 1 drop/7 seconds

Q2. A modern grand-prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is μs, then the magnitude of negative lift FL acting downwards on the car is: (1) m( μsRv2 + g) (2) m( μsRv2 −g) (3) m(g − μsRv2 ) (4) −m(g + μsRv2 )

Q2. If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density: (1) [FL−4 T2] (2) [FL−3 T3] (3) [FL−3 T2] (4) [FL−5 T2]

Q2. If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately : (Take : g = 10 ms−2 , the radius of earth, R = 6400 × 103 m, Take π = 3. 14 ) (1) 60 minutes (2) does not change (3) 1200 minutes (4) 84 minutes

Q2. The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt The dimensional formula of AD is: B (1) [M0 L T−1] (2) [ML2 T−3] (3) [M1 L1 T−2] (4) [M2 L2 T−3]

Q2. A butterfly is flying with a velocity 4√2 m s−1 in north-east direction. Wind is slowly blowing at 1 m s−1 from north to south. The resultant displacement of the butterfly in 3 seconds is: (1) 3 m (2) 20 m (3) 12√2 m (4) 15 m

Q2. If C and V represent capacity and voltage respectively then what are the dimensions of λ where C/V = λ ? (1) [M−2 L−4 I3 T7] (2) [M−2 L−3I2 T6] (3) [M−1 L−3I−2 T−7] (4) [M−3 L−4I3 T7]

Q2. If E and H represents the intensity of electric field and magnetizing field respectively, then the unit of HE will be: (1) joule (2) ohm (3) newton (4) mho

Q2. If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph? (1) (2) (3) (4)

Q2. Match List I with List II. List-I List-II a Capacitance, C i M1 L1 T−3 A−1 b Permittivity of free space, ε0 ii M−1 L−3 T4 A2 c Permeability of free space, μ0 iii M−1 L−2 T4 A2 d Electric field, E iv M1L1T−2A−2 Choose the correct answer from the options given below (1) (a ) → (iii ), ( b ) →(ii), (c) →(iv), (d) → (i) (2) (a ) → (iii ), ( b ) → (iv ), ( c ) → (ii ), ( d ) → (i) (3) (a ) → (iv ), ( b ) → (ii ), ( c ) → (iii ), ( d ) →(4)(i)(a ) → (iv ), ( b ) → (iii ), ( c ) → (ii ), ( d ) → (i)

Q3. The relation between time t and distance x for a moving body is given as t = mx2 + nx, where m and n are constants. The retardation of the motion is: (When v stands for velocity) (1) 2mv3 (2) 2mnv3 (3) 2nv3 (4) 2n2v3

Q3. A sphere of radius a and mass m rolls along a horizontal plane with constant speed v0 . It encounters an inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel? 0 (1) 2 v2 0 (2) 7v2 5 g sin θ 10 g sin θ 0 (3) v2 0 (4) v2 5g sin θ 2g sin θ