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Motion in a Plane Test 7

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Motion in a Plane Test 7
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  • Question 1
    1 / -0

    Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

    Assertion : If dot product and cross product of A and B are zero, it implies that one of the vector A and B must be a null vector

    Reason : Null vector is a vector with zero magnitude.

    Solution

    If →A and →B are not null Vectors then it follows that sinθ and cosθ both should be zero simultaneously. But it cannot be possible so it is essential that one of the vectors must be a null vector.

  • Question 2
    1 / -0

    Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

    Assertion: A physical quantity cannot be called as a vector if its magnitude is zero.

    Reason: A vector has both magnitude and direction.

    Solution

    If a vector quantity has zero magnitude then it is called a null vector. That quantity may have some direction even if its magnitude is zero.

  • Question 3
    1 / -0

    Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

    Assertion : If A.B= B.C, then A may not always be equal to C.

    Reason : The dot product of two vectors involves cosine of the angle between the two vectors.

    Solution

  • Question 4
    1 / -0

    Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

    Assertion : The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously from same point on one bank may reach opposite bank simultaneously moving along different paths.

    Reason : For boats to cross the river in same time. The component of their velocity relative to river in direction normal to flow should be same.

    Solution

    If component of velocity of boat relative to river is same normal to river flow (as shown in figure) both boats reach other bank simultaneously since this component is responsible for reaching the other bank of the river.

  • Question 5
    1 / -0

    Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

    Assertion : τ=r x F and τ=F x r

    Reason : Cross product of vectors is commutative.

    Solution

    Cross-product of two vectors is anticommutative.

    Cross product of vectors is not commutative.

  • Question 6
    1 / -0

    Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

    Assertion : If there were no gravitational force, the path of the projected body always be a straight line.

    Reason : Gravitational force makes the path of projected body always parabolic.

    Solution

    Upto ordinary heights, the gravitational force remains stationary, since the distance from earth's surface is negligible compared to radius of the earth. Thus the path of projectiles is parabolic.

    However as the distance increases, the gravitational field decreases inversely as square of distance from earth. Thus the gravitational field is variable. Under such a gravitational field, the path of projectile is elliptical.

  • Question 7
    1 / -0

    Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

    Assertion : Two balls of different masses are thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed.

    Reason : The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.

    Solution

    Let the balls be thrown vertically upward with speed u.

    Using

    Therefore, the Maximum height,

    Also using

    Thus the balls will pass through the point of projection in downward direction with the same speed (v). Also from the equations used, the maximum height and the downward velocity attained are independent of mass of the ball.

  • Question 8
    1 / -0

    Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

    Assertion : If a body of mass m is projected upwards with a speed V making an angle ? with the vertical, than the change in the momentum of the body along X–axis is zero.

    Reason : Mass of the body remains constant along X–axis

    Solution

    When a body is projected up making an angle ? the velocity component along-axis remains constant. Therefore, Momentum along x-axis is constant. Along horizontal, mass and velocity both are constant.

  • Question 9
    1 / -0

    Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

    Assertion : Minimum number of non-equal vectors in a plane required to give zero resultant is three.

    Reason : If sum of vectors A+B+C=0 , then they must lie in one plane.

    Solution

    As the vectors are non-equal so two vector can not make zero resultant. According to triangle law of vector addition at least 3 vectors are needed to make zero resultant. Thus, we can say that statement -2 is the reason of statement -1.

  • Question 10
    1 / -0

    Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

    Assertion : The scalar product of two vectors can be zero.

    Reason : If two vectors are perpendicular to each other, their scalar product will be zero.

    Solution

    If θ be the angle between two vectors , then their scalar product,

    If θ = 90 degrees then

    I.e. if are perpendicular to each other then their scalar product will be zero.

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