JEE Advanced (Fill in the Blanks): Motion | Chapter-wise Tests for JEE Main & Advanced PDF Download

Fill in the Blanks

Q.1. A particle moves in a circle of radius R. In half the period of revolution its displacement is ____________and distance covered is ________.   (1983 - 2 Marks)

Ans. 2R, πR

Solution. Displacement = AOB = 2 R

Displacement = AOB = 2 R

Q.2. Four persons K, L, M, N are initially at the four corners of a square of side d. Each person now moves with a uniform speed v in such a way that K always moves directly towards L, L directly towards M, M directly towards N, and N directly towards K. The four persons will meet at a time ..............           (1984- 2 Marks)

Ans. d/v

Solution. The relative velocity of K w.r.t L along the line KL is

(∴ the component of velocity of L along KL is zero)

The displacement of K till K and L meet is d.

∴ Time taken for K and L to meet will be = d/v

Q.3. Spotlight S rotates in a horizontal plane with constant angular velocity of 0.1 radian/second. The spot of light P moves along the wall at a distance of 3 m. The velocity of the spot P when q = 45° (see fig.) is ................. m/s        (1987 - 2 Marks)

Ans. 0.6 m/s

Solution. 

The velocity (v) of spot = dx / dt

and the angular speed (w) of spot light  =d∅/dt

FromΔSOP,

∴ v = 3 sec² 45° × 0.1       [∴ q + φ= 90° ]
∴ v = 3 × 2 × 0.1 = 0.6 m/s

B True/False

Q.1. Two balls  of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed (Neglect air resistance).                  (1983 - 2 Marks)

Ans. T

Solution. When the two balls are thrown vertically upwards with the same speed u then their final speed v at the point of projection is v² – u² = 2 × g × s

 Here, s = 0 

∴ v = u for both the cases

Q.2. A projectile fired from the ground follows a parabolic path.

The speed of the projectile is minimum at the top of its path.         (1984 - 2 Marks)

Ans. T

Solution. T.E. = P.E. + K.E.

T.E. = Constant

 At P, K.E. is minimum and P.E. is maximum. Since K.E. is minimum speed is also minimum.

Q.3. 

Two iden tical trains are moving on r ails along the equator on the earth in opposite directions with the same speed.

They will exert the same pressure on the rails.         (1985 - 3 Marks)

Ans. F

Solution. The pressure exerted will be different because one train is moving in the direction of earth’s rotation and other  in the opposite direction.