Is it
My grandmother 'read' the newspaper last night
My grandmother was reading the newspaper last night?

Both of them are correct. But using the sentence "My grandmother was reading the newspaper last night" would be more appropriate. 
Ten people were sitting around the table. It was raining outside. Suddenly, the door opened and a woman entered the room. She was wearing a black dress. Everyone stared at, her but she didn't say anything. She slowly went to the table and put an envelope on it. They were just staring at her as she left the room.
Note the difference between these two sentences from the story:

Everyone stared at her.
They were just staring at her.
The past simple in the first sentence expresses a momentary, comp
U r right !
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The correct one is My Grandmother was reading the newspaper last night.
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Well, it's both (if it's not shocking)!

These two sentences make use of two types of past tenses.
One - past perfect tense.
Another - past continuous tense.

Whatever. But, both the sentences convey the same meaning, with a slight difference. Anyways, both sentences are grammatically correct. The sentence-structure and all.

There isn't any option like this one is correct and the other is not.

It's just that both the sentences in past tense convey a slightly different meaning. 
Each are two different CORRECT sentences which convey a differnt meaning.

I hope I was able to get to the point.

Now,  I will provide the explanation. What do the two sentences each mean?

PAST TENSE - It means something happenned in the past. By 'something', I refer to any event, action, or stuff like this. 'Something' has been completed in the past. It has completed taking place, already.

So, the first sentence 
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