Work done by a constant force $\vec{F}$ on a body that undergoes a displacement $\vec{d}$ is given by the dot product: $W = \vec{F} \cdot \vec{d} = | \vec{F}| |\vec{d}| \cos \theta$, where $\theta$ is the angle between the force and displacement vectors. Work is negative when $\cos \theta$ is negative. This occurs when the angle $\theta$ is between 90° and 270° (exclusive of 90° and 270° where work is zero). Let's examine the options: A) Angle is 135°. $\cos 135° = -1/\sqrt{2}$. Since $\cos \theta$ is negative, the work done is negative. B) Angle is 0° (same direction) or 180° (opposite direction). If $ \theta=0°$, $\cos 0° = 1$, work is positive. If $ \theta=180°$, $\cos 180° = -1$, work is negative. So, parallel force and displacement can result in negative work (if opposite directions), but doesn't always. C) Angle is 90°. $\cos 90° = 0$. Work is zero. D) Angle is 45°. $\cos 45° = 1/\sqrt{2}$. Since $\cos \theta$ is positive, work is positive. Option A is the only situation listed that guarantees the work done by the applied force is negative.
In which of the following situations will an applied force do negative work on a body?
Asked in UPSC Geoscientist 2023 · Topic: Mechanics (Work, Energy, and Power)
Show answer
Answer: A. The applied force and displacement of the body are at 135° to each other
More Physics questions
- A frictionless pulley has a rope of negligible mass passing over it. Blocks of mass 15 kg and 5 kg are attached at the two ends of the rope and held stationary. When the masses are released to move freely, their speed in m s-1, after the rope has slipped by 0.25 m over the pulley, is closest to : (take g = 10.0 m s-2)
- A ball of mass 100 g falls freely from a height of h = 20 m and hits the ground at a speed of 1·4 √gh. Take g = 10 m s⁻². Which one among the following is the correct value of the work done on the ball by air friction ?
- A spherical ball is divided into two equal halves. If the curved surface area of each half is 56.57 cm², then what is the volume of the spherical ball? [π = 3.14]
- The volume of globe varies as the cube of its radius. Three solid globes of diameters 1$ \frac{1}{2}$, 2 and 2$\frac{1}{2}$ metres are melted and formed into a new solid globe. What is the diameter of the new globe?
- If a> 0 and a*—62a>+ 1 =0, what is the value of a*> + 1/a® ?
- A simple machine helps a person in doing :
- एक सिाधारण मशीन, एक व्ǔक्त को क्ा करने में सिहाता करती है ?
- A person carrying a bag of total mass 25 kg climbs upto a height 5 meters in 30 seconds. How much power the man needs to carry the bag ?