Practice Questions

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 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. 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)

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. The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by : (1) (2) (3) (4)

Q2. If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor: (1) 12 , 2√2 (2) 41 , √2 (3) 14 , 2√2 (4) 21 , √2

Q2. A ball is thrown up with a certain velocity so that it reaches a height h. Find the ratio of the two different times of the ball reaching h in both the directions. 3 (1) √2−1 (2) 1 √2+1 3 (3) √3−√2 (4) √3−1 √3+√2 √3+1

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. An object of mass 𝑚 is being moved with a constant velocity under the action of an applied force of 2 N along a frictionless surface with following surface profile. The correct applied force vs distance graph will be : (1) (2) (3) (4)

Q2. If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL2M −5G−2 are: (1) [M1L1 T−2] (2) [M0 L1 T0] (3) [M−1L−1T2] (4) [M0 L0 T0]

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. 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. Match List - I with List - II : List −I List −II (a) h (Planck's constant) (i) [MLT−1] (b) E (kinetic energy) (ii) [ML2 T−1] (c) V (electric potential) (iii) [ML2 T−2] (d) P (linear momentum) (iv) [ML2 I−1 T−3] Choose the correct answer from the options given below: (1) (a) →(ii), (b) →(iii), (c) →(iv), (d) →(i) (2) (a) →(i), (b) →(ii), (c) →(iv), (d) →(iii) (3) (a) →(iii), (b) →(ii), (c) →(iv), (d) →(i) (4) (a) →(iii), (b) →(iv), (c) →(ii), (d) →(i)

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. 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 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. 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 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

Q3. A scooter accelerates from rest for time t1 at constant rate a1 and then retards at constant rate a2 for time t2 and comes to rest. The correct value of t1 will be : t2 (1) a2 (2) a1 a1 a2 (3) a1+a2 (4) a1+a2 a1 a2

Q3. If velocity 𝑉 time 𝑇 and force 𝐹 are chosen as the base quantities, the dimensions of the mass will be : (1) 𝐹𝑉𝑇-1 (2) 𝐹𝑇-1𝑉-1 (3) 𝐹𝑇2 𝑉 (4) 𝐹𝑇𝑉-1

Q3. A circular hole of radius ( a2 ) is cut out of a circular disc of radius a as shown in figure. The centroid of the remaining circular portion with respect to point O will be: (1) 2 a (2) 5 a 3 6 (3) 1 a (4) 10 a 6 11

Q3. Match List - I with List - II : List - I List - II a Magnetic induction i ML2 T−2 A−1 b Magnetic flux ii M0 L−1 A c Magnetic permeability iii MT−2 A−1 d Magnetization iv MLT−2 A−2 Choose the most appropriate answer from the options given below : (1) (a) −(iii), (b) −(ii), (c) −(iv), (d) −(i) (2) (a) −(iii), (b) −(i), (c) −(iv), (d) −(ii) (3) (a) −(ii), (b) −(iv), (c) −(i), (d) −(iii) (4) (a) −(ii), (b) −(i), (c) −(iv), (d) −(iii)

Q3. Moment of inertia M . I . of four bodies, having same mass and radius, are reported as; 𝐼1 = M . I . of thin circular ring about its diameter, 𝐼2 = M . I . of circular disc about an axis perpendicular to disc and going through the centre, 𝐼3 = M . I . of solid cylinder about its axis and 𝐼4 = M . I . of solid sphere about its diameter. Then: 5 (1) 𝐼1 + 𝐼2 = 𝐼3 + 2𝐼4. (2) 𝐼1 + 𝐼3 < 𝐼2 + 𝐼4 (3) 𝐼1 = 𝐼2 = 𝐼3 > 𝐼4 (4) 𝐼1 = 𝐼2 = 𝐼3 < 𝐼4

Q3. The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of, 20 m s−2 . The gases come out at a relative speed of 500 m s−1 , with respect to the rocket: [Use g = 10 m s−2] (1) 10 kg s−1 (2) 60 kg s−1 (3) 500 kg s−1 (4) 6. 0 × 102 kg s−1

Q3. The motion of a mass on a spring, with spring constant K is as shown in figure. The equation of motion is given by, x(t) = A sin ωt+B cos ωt with ω = . √Km Suppose that at time t = 0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t) = C cos(ωt −ϕ), where C and ϕ are (1) v(0) (2) x(0)ω + ϕ = C = √2v(0)2ω2 ω2 x(0)2, tan−1( 2v(0) ) + x(0)2, ϕ = tan−1( x(0)ω ) C = √2v(0)2 (3) x(0)ω (4) v(0) C = + ϕ = C = + ϕ = ω2 x(0)2, tan−1( x(0)ω ) ω2 x(0)2, tan−1( v(0) ) √v(0)2 √v(0)2