Practice Questions

Q1. Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R) Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is ρ and radius of the drop is r, then T = 3 is dimensionally correct, where K is dimensionless. K√ρr3S 2 Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period. In the light of above statements, choose the correct answer from the options given below. (1) Both (A) and (R) are true and (R) is the correct explanation of (A) (2) Both (A) and (R) are true but (R) is not the correct explanation of (A) (3) (A) is true but (R) is false (4) (A) is false but (R) is true

Q1. A person moved from 𝐴 to 𝐵 on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be : (Given cos135° = - 0 . 7) (1) 42 m (2) 47 m (3) 19 m (4) 40 m

Q1. An expression of energy density is given by u = αβ sin( αxkt ), where α, β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be (1) [ML2 T−2θ−1] (2) [M0L2T−2] (3) [M0L0T0] (4) [M0L2T0]

Q1. Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as v2 = m2n v1 and a2 = mna1 respectively. Here m and n are constants. The relations for distance and time in two systems respectively are n2 n3 (1) = m T 2 m3 L1 = L2 and n2m T 1 = T2 (2) L1 = m2n4 L2 and T1 (3) L1 = n2m L2 and T1 = m2n4 T2 (4) n2m L1 = L2 and m2n4 T 1 = T2

Q1. A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in t s , the distance travelled by the toy in the next t s will be: (1) 10 m (2) 20 m (3) 30 m (4) 40 m

Q1. Identify the pair of physical quantities which have different dimensions: (1) Wave number and Rydberg's constant (2) Stress and Coefficient of elasticity (3) Coercivity and Magnetisation (4) Specific heat capacity and Latent heat

Q1. A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of (1) 15% (2) 25% (3) 75% (4) 5%

Q2. Two masses 𝑀1 and 𝑀2 are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass 𝑀2 is twice that of 𝑀1. the acceleration of the system is 𝑎1. When the mass 𝑎1 𝑀2 is thrice that of 𝑀1. The acceleration of The system is 𝑎2. The ratio will be 𝑎2 (1) 1 (2) 2 3 3 3 1 (3) (4) 2 2

Q2. A ball is spun with angular acceleration α = 6t2 −2t where t is in second and α is in rad s−2 . At t = 0, the ball has angular velocity of 10 rad s−1 and angular position of 4 rad . The most appropriate expression for the angular position of the ball is (1) 3 t4 −t2 + 10t (2) t4 2 2 −t33 + 10t + 4 (3) 2t4 3 −t36 + 10t + 12 (4) 2t4 −t32 + 5t + 4

Q2. In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement? (1) 4a1 + 2a2 + a3 + a4 = 0 (2) a1 + 4a2 + 3a3 + a4 = 0 (3) a1 + 4a2 + 3a3 + 2a4 = 0 (4) 2a1 + 2a2 + 3a3 + a4 = 0

Q2. A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height h while going up and coming down respectively. 3 (1) √2−1 (2) √3−√2 √2+1 √3+√2 (3) √3−1 (4) 1 √3+1 3

Q2. A bullet is shot vertically downwards with an initial velocity of 100 m s−1 from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time t = 20 s will be : (Take g = 10 m s−2 ) (1) (2) (3) (4)

Q2. A projectile is projected with velocity of 25 m s−1 at an angle θ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of θ will be : [use use g = 10 m s−2 ] (1) 1 5t2 (2) 1 4R 2 sin−1( 4R ) 2 sin−1( 5t2 ) (3) tan−1( 4t25R ) (4) cot−1( 20t2R )

Q2. A projectile is launched at an angle α with the horizontal with a velocity 20 m s−1 . After 10 s , its inclination with horizontal is β . The value of tan β will be : (g = 10 m s−2) . (1) tan α + 5 sec α (2) tan α −5 sec α (3) 2 tan α −5 sec α (4) 2 tan α + 5 sec α

Q2. If momentum 𝑃, area 𝐴 and time 𝑇 are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is (1) PA-1T0 (2) PAT-1 (3) PA-1T (4) PA-1T-1

Q2. In van dar Wall equation [P ][V T is temperature. The ratio of constants ab is dimensionally equal to : (1) P (2) V V P (3) PV (4) PV 3

Q2. Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Two identical balls 𝐴 and 𝐵 thrown with same velocity '𝑢' at two different angles with horizontal attained the same range 𝑅. If A and 𝐵 reached the maximum height ℎ1 and ℎ2 respectively, then 𝑅= 4√ℎ1ℎ2 𝑢2sin2𝜃 𝑢2cos2𝜃 Reason R: Product of said heights. ℎ1ℎ2 = 2𝑔 · 2𝑔 (1) Both A and R are true and R is the correct (2) Both A and R are true but R is NOT the correct explanation of A. explanation of A. (3) A is true but R is false. (4) A is false but R is true.

Q2. An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 m s−2 ]. (1) 1 : 1 (2) √2 : √3 (3) √3 : √2 (4) 2 : 3

Q2. The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is (1) 2. 0 (2) 1. 0 (3) 0. 5 (4) 1. 5

Q2. Three masses M = 100 kg, m1 = 10 kg and m2 = 20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m2 moves upward with an acceleration of 2 ms−2 . The value of F is (Take g = 10 ms−2 ) (1) 3360 N (2) 3380 N (3) 3120N (4) 3240N

Q2. A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws 𝑛 balls per second, the maximum height the balls can reach is 𝑔 𝑔 (1) (2) 2𝑛 𝑛 (3) 2𝑔𝑛 (4) 𝑔 2𝑛2

Q3. A bag is gently dropped on a conveyor belt moving at a speed of 2 m s−1 . The coefficient of friction between the conveyor belt and bag is 0. 4 Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is : [Take g = 10 m s−2 ] (1) 2 m (2) 0. 5 m (3) 3. 2 m (4) 0. 8 ms

Q3. A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4 . 5 cm s-1. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne). (1) 3 (2) 9 (3) 12 (4) 18

Q3. A ball is released from a height ℎ. If 𝑡1 and 𝑡2 be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between 𝑡1 and 𝑡2. (1) 𝑡1 = √2𝑡2 (2) 𝑡1 = √2 - 1𝑡2 (3) 𝑡2 = √2 + 1𝑡1 (4) 𝑡2 = √2 - 1𝑡1

Q3. If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time? (1) √LC (2) RL (3) CR (4) CL