Question

A projectile is fired from the surface of the earth with a velocity of $$5\,m{s^{ - 1}}$$  and angle $$\theta $$ with the horizontal. Another projectile fired from another planet with a velocity of $$3\,m{s^{ - 1}}$$  at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $$m{s^{ - 2}}$$ ) given $$g = 9.8\,m/{s^2}$$

A. 3.5  
B. 5.9
C. 16.3
D. 110.8
Answer :   3.5
Solution :
Horizontal range $$ = \frac{{{u^2}\sin 2\theta }}{g}\,{\text{so}}\,g \propto {u^2}$$
$${\text{or}}\,\,\frac{{{g_{{\text{planet}}}}}}{{{g_{{\text{earth}}}}}} = \frac{{{{\left( {{u_{{\text{planet}}}}} \right)}^2}}}{{{{\left( {{u_{{\text{earth}}}}} \right)}^2}}}$$
Therefore $${g_{{\text{planet}}}} = {\left( {\frac{3}{5}} \right)^2}{\left( {9.8\,m/s} \right)^2}$$
$$ = 3.5\,m/{s^2}$$

Releted MCQ Question on
Basic Physics >> Kinematics

Releted Question 1

A river is flowing from west to east at a speed of $$5$$ metres per minute. A man on the south bank of the river, capable of swimming at $$10$$ metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction-

A. Due north
B. $${30^ \circ }$$ East of north
C. $${30^ \circ }$$ West of north
D. $${60^ \circ }$$ East of north
Releted Question 2

A boat which has a speed of $$5 km/hr$$   in still water crosses a river of width $$1 \,km$$  along the shortest possible path in $$15 \,minutes.$$   The velocity of the river water in $$km/hr$$  is-

A. 1
B. 3
C. 4
D. $$\sqrt {41} $$
Releted Question 3

In $$1.0\,s,$$  a particle goes from point $$A$$  to point $$B,$$  moving in a semicircle of radius $$1.0 \,m$$  (see Figure). The magnitude of the average velocity-
Kinematics mcq question image

A. $$3.14 \,m/s$$
B. $$2.0 \,m/s$$
C. $$1.0 \,m/s$$
D. Zero
Releted Question 4

A ball is dropped vertically from a height $$d$$ above the ground. It hits the ground and bounces up vertically to a height $$\frac{d}{2}.$$  Neglecting subsequent motion and air resistance, its velocity $$v$$  varies with the height $$h$$  above the ground as-

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B. Kinematics mcq option image
C. Kinematics mcq option image
D. Kinematics mcq option image

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