Practice Questions

Q1. If the percentage errors in measuring the length and the diameter of a wire are 0 . 1% each. The percentage error in measuring its resistance will be: (1) 0 . 2% (2) 0 . 3% (3) 0 . 1% (4) 0 . 144% Q2. 1 𝑏2 A force is represented by 𝐹= 𝑎𝑥2 + 𝑏𝑡 2, where 𝑥= distance and 𝑡= time. The dimensions of are : 𝑎 (1) [𝑀𝐿3 𝑇 – 3 ] (2) [𝑀𝐿𝑇– 2] (3) [𝑀𝐿– 1 𝑇– 1] (4) [𝑀𝐿2 𝑇– 3]

Q1. If two vectors →𝐴 and →𝐵 having equal magnitude 𝑅 are inclined at an angle 𝜃, then 𝜃 2𝑅sin (1) →𝐴− →𝐵= √2𝑅sin 𝜃2 (2) →𝐴+ →𝐵= 2 → → 𝜃 → → 𝜃 (3) 𝐴+ 𝐵= 2𝑅cos (4) 𝐴− 𝐵= 2𝑅cos 2 2

Q1. The resistance R = VI , where V = (200 ± 5) V and I = (20 ± 0. 2) A, the percentage error in the measurement of R is : (1) 3. 5% (2) 7% (3) 3% (4) 5. 5%

Q1. The dimensional formula of latent heat is : (1) [ML2 T−2] (2) [M0 L2 T−2] (3) [MLT−2] (4) [M∘LT−2]

Q1. The angle between vector →Q and the resultant of (2→Q + 2→P) and (2→Q −2→P) is : (1) (2→Q−2 →P) (2) 0∘ tan−1 2→Q+2 →P (3) tan−1(P/Q) (4) tan−1(2Q/P)

Q1. The equation of state of a real gas is given by 𝑃+ 𝑎 (𝑉- 𝑏) = 𝑅𝑇, where 𝑃, 𝑉 and 𝑇 are pressure, volume 𝑉2 a and temperature respectively and 𝑅 is the universal gas constant. The dimensions of is similar to that of : b2 (1) 𝑃𝑉 (2) 𝑃 (3) 𝑅𝑇 (4) 𝑅

Q1. Match List - I with List - II. List - I (Number) List - II (Signficant figure) (A) 1001 (I) 3 (B) 010 . 1 (II) 4 (C) 100 . 100 (III) 5 (D) 0 . 0010010 (IV) 6 Choose the correct answer from the options given below: (1) (A)-(III), (B)-(IV), (C)-(II), (D)-(I) (2) (A)-(IV), (B)-(III), (C)-(I), (D)-(II) (3) (A)-(II), (B)-(I), (C)-(IV), (D)-(III) (4) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Q1. Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit. (1) T 2 = 4π2r2GM (2) T 2 = GM4π2r2 (3) T 2 = 4π2r3GM (4) T 2 = 4π2r3

Q1. A physical quantity Q is found to depend on quantities a, b, c by the relation Q = a4b3 . The percentage error in c2 a, b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is: (1) 66% (2) 43% (3) 34% (4) 14%

Q1. The de-Broglie wavelength associated with a particle of mass m and energy E is h/√2mE . The dimensional formula for Planck's constant is : (1) [ML2 T−1] (2) [ML−1 T−2] (3) [MLT−2] (4) [M2 L2 T−2]

Q2. A particle is moving in a straight line. The variation of position x as a function of time t is given as x = (t3 −6t2 + 20t + 15) m. The velocity of the body when its acceleration becomes zero is: (1) 4 m s−1 (2) 8 m s−1 (3) 10 m s−1 (4) 6 m s−1

Q2. The angle of projection for a projectile to have same horizontal range and maximum height is : (1) tan−1(4) (2) tan−1 ( 14 ) (3) tan−1 ( 21 ) (4) tan−1(2)

Q2. What is the dimensional formula of ab−1 in the equation (P + V2a )(V −b) = RT, where letters have their usual meaning. (1) [M−1 L5 T3] (2) [M6 L7 T4] (3) [ML2 T−2] (4) [M0 L3 T−2]

Q2. The dimensional formula of angular impulse is : (1) [M L – 2T – 1] (2) [M L2 T – 2 ] (3) [M L T – 1 ] (4) [M L2 T – 1 ]

Q2. A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is: (1) √8 km (2) 8 km (3) 6 km (4) 4 km

Q2. Position of an ant ( S in metres) moving in Y −Z plane is given by S = 2t2ˆj + 5ˆk (where t is in second). The magnitude and direction of velocity of the ant at t = 1 s will be : (1) 16 m s−1 in y-direction (2) 4 m s−1 in x-direction (3) 9 m s−1 in z-direction (4) 4 m s−1 in y-direction

Q2. Train A is moving along two parallel rail tracks towards north with 72 km h-1 and train 𝐵 is moving towards south with speed 108 km h-1. Velocity of train 𝐵 with respect to 𝐴 and velocity of ground with respect to 𝐵 are (in m s-1): (1) -30 and 50 (2) -50 and -30 (3) -50 and 30 (4) 50 and -30

Q3. Three blocks 𝐴, 𝐵 and 𝐶 are pulled on a horizontal smooth surface by a force of 80 N as shown in figure. The tensions 𝑇1 and 𝑇2 in the string are respectively: (1) 40N, 64N (2) 60N, 80N (3) 88N, 96N (4) 80N, 100N

Q3. If the radius of curvature of the path of two particles of same mass are in the ratio 3 : 4, then in order to have constant centripetal force, their velocities will be in the ratio of: (1) √3 : 2 (2) 1 : √3 (3) √3 : 1 (4) 2 : √3

Q3. A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if g = 10 m/s2 ) : (1) 100 N (2) 200 N (3) 300 N (4) 150 N

Q3. A cricket player catches a ball of mass 120 g moving with 25 m s-1 speed. If the catching process is completed in 0 . 1 s then the magnitude of force exerted by the ball on the hand of player will be(in SI unit): (1) 24 (2) 12 (3) 25 (4) 30

Q3. A light string passing over a smooth light fixed pulley connects two blocks of masses 𝑚1 and 𝑚2. If the 𝑔 acceleration of the system is 8, then the ratio of masses is (1) 9 (2) 8 7 1 4 5 (3) (4) 3 3

Q3. A 2 kg brick begins to slide over a surface which is inclined at an angle of 45∘ with respect to horizontal axis. The co-efficient of static friction between their surfaces is: (1) 1.7 (2) 1 √3 (3) 0.5 (4) 1

Q4. A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω. If another disc of same dimensions but of mass M/2 is placed gently on the first disc co-axially, then the new angular velocity of the system is : (1) 3 ω (2) 5 ω 2 4 (3) 2 ω (4) 4 ω 3 5

Q4. A stationary particle breaks into two parts of masses mA and mB which move with velocities vA and vB respectively. The ratio of their kinetic energies (KB : KA) is : (1) vB : vA (2) mB : mA (3) mBvB : mAvA (4) 1 : 1